6x2-18x-36=100

Solution for 6x2-18x-36=100 equation:

6x^2-18x-36=100

We move all terms to the left:

6x^2-18x-36-(100)=0

We add all the numbers together, and all the variables

6x^2-18x-136=0

a = 6; b = -18; c = -136;
Δ = b2-4ac
Δ = -182-4·6·(-136)
Δ = 3588
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:

$\sqrt{\Delta}=\sqrt{3588}=\sqrt{4*897}=\sqrt{4}*\sqrt{897}=2\sqrt{897}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{897}}{2*6}=\frac{18-2\sqrt{897}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{897}}{2*6}=\frac{18+2\sqrt{897}}{12}
$