0=4x^2+2x-72

Solution for 0=4x^2+2x-72 equation:

0=4x^2+2x-72

We move all terms to the left:

0-(4x^2+2x-72)=0

We add all the numbers together, and all the variables

-(4x^2+2x-72)=0

We get rid of parentheses

-4x^2-2x+72=0

a = -4; b = -2; c = +72;
Δ = b2-4ac
Δ = -22-4·(-4)·72
Δ = 1156
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1156}=34$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-34}{2*-4}=\frac{-32}{-8}
=+4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+34}{2*-4}=\frac{36}{-8}
=-4+1/2
$