4x^2-6x-36=72

Solution for 4x^2-6x-36=72 equation:

4x^2-6x-36=72

We move all terms to the left:

4x^2-6x-36-(72)=0

We add all the numbers together, and all the variables

4x^2-6x-108=0

a = 4; b = -6; c = -108;
Δ = b2-4ac
Δ = -62-4·4·(-108)
Δ = 1764
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1764}=42$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-42}{2*4}=\frac{-36}{8}
=-4+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+42}{2*4}=\frac{48}{8}
=6
$