36x^2=-24x+7

Solution for 36x^2=-24x+7 equation:

36x^2=-24x+7

We move all terms to the left:

36x^2-(-24x+7)=0

We get rid of parentheses

36x^2+24x-7=0

a = 36; b = 24; c = -7;
Δ = b2-4ac
Δ = 242-4·36·(-7)
Δ = 1584
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1584}=\sqrt{144*11}=\sqrt{144}*\sqrt{11}=12\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-12\sqrt{11}}{2*36}=\frac{-24-12\sqrt{11}}{72}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+12\sqrt{11}}{2*36}=\frac{-24+12\sqrt{11}}{72}
$