6x^2-120=36x

Solution for 6x^2-120=36x equation:

6x^2-120=36x

We move all terms to the left:

6x^2-120-(36x)=0

a = 6; b = -36; c = -120;
Δ = b2-4ac
Δ = -362-4·6·(-120)
Δ = 4176
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:

$\sqrt{\Delta}=\sqrt{4176}=\sqrt{144*29}=\sqrt{144}*\sqrt{29}=12\sqrt{29}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-12\sqrt{29}}{2*6}=\frac{36-12\sqrt{29}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+12\sqrt{29}}{2*6}=\frac{36+12\sqrt{29}}{12}
$