6x2+36=36x

Solution for 6x2+36=36x equation:

6x^2+36=36x

We move all terms to the left:

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

a = 6; b = -36; c = +36;
Δ = b2-4ac
Δ = -362-4·6·36
Δ = 432
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:

$\sqrt{\Delta}=\sqrt{432}=\sqrt{144*3}=\sqrt{144}*\sqrt{3}=12\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-12\sqrt{3}}{2*6}=\frac{36-12\sqrt{3}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+12\sqrt{3}}{2*6}=\frac{36+12\sqrt{3}}{12}
$