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Question
6x^{2}=13x+5
Solve the quadratic equation
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Solve by factoring
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Solve using the quadratic formula
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Solve by completing the square
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Solve using the PQ formula
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x_{1}=-\frac{1}{3},x_{2}=\frac{5}{2}
Alternative Form
x_{1}=-0.\dot{3},x_{2}=2.5
Evaluate
6x^{2}=13x+5
Move the expression to the left side
6x^{2}-13x-5=0
Factor the expression
More Steps
Evaluate
6x^{2}-13x-5
Rewrite the expression
6x^{2}+\left(2-15\right)x-5
Calculate
6x^{2}+2x-15x-5
Rewrite the expression
2x\times 3x+2x-5\times 3x-5
\text{Factor out }2x\text{ from the expression}
2x\left(3x+1\right)-5\times 3x-5
\text{Factor out }-5\text{ from the expression}
2x\left(3x+1\right)-5\left(3x+1\right)
\text{Factor out }3x+1\text{ from the expression}
\left(2x-5\right)\left(3x+1\right)
\left(2x-5\right)\left(3x+1\right)=0
When the product of factors equals 0,at least one factor is 0
\begin{align}&2x-5=0\\&3x+1=0\end{align}
\text{Solve the equation for }x
More Steps
Evaluate
2x-5=0
Move the constant to the right-hand side and change its sign
2x=0+5
Removing 0 doesn't change the value,so remove it from the expression
2x=5
Divide both sides
\frac{2x}{2}=\frac{5}{2}
Divide the numbers
x=\frac{5}{2}
\begin{align}&x=\frac{5}{2}\\&3x+1=0\end{align}
\text{Solve the equation for }x
More Steps
Evaluate
3x+1=0
Move the constant to the right-hand side and change its sign
3x=0-1
Removing 0 doesn't change the value,so remove it from the expression
3x=-1
Divide both sides
\frac{3x}{3}=\frac{-1}{3}
Divide the numbers
x=\frac{-1}{3}
\text{Use }\frac{-a}{b}=\frac{a}{-b}=-\frac{a}{b}\text{ to rewrite the fraction}
x=-\frac{1}{3}
\begin{align}&x=\frac{5}{2}\\&x=-\frac{1}{3}\end{align}
Solution
x_{1}=-\frac{1}{3},x_{2}=\frac{5}{2}
Alternative Form
x_{1}=-0.\dot{3},x_{2}=2.5
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