3x^2=23x-36

Solution for 3x^2=23x-36 equation:

3x^2=23x-36

We move all terms to the left:

3x^2-(23x-36)=0

We get rid of parentheses

3x^2-23x+36=0

a = 3; b = -23; c = +36;
Δ = b2-4ac
Δ = -232-4·3·36
Δ = 97
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-23)-\sqrt{97}}{2*3}=\frac{23-\sqrt{97}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+\sqrt{97}}{2*3}=\frac{23+\sqrt{97}}{6}
$