12x^2-18x=36

Solution for 12x^2-18x=36 equation:

12x^2-18x=36

We move all terms to the left:

12x^2-18x-(36)=0

a = 12; b = -18; c = -36;
Δ = b2-4ac
Δ = -182-4·12·(-36)
Δ = 2052
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:

$\sqrt{\Delta}=\sqrt{2052}=\sqrt{36*57}=\sqrt{36}*\sqrt{57}=6\sqrt{57}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-6\sqrt{57}}{2*12}=\frac{18-6\sqrt{57}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+6\sqrt{57}}{2*12}=\frac{18+6\sqrt{57}}{24}
$