0=2x^2+2x-144

Solution for 0=2x^2+2x-144 equation:

0=2x^2+2x-144

We move all terms to the left:

0-(2x^2+2x-144)=0

We add all the numbers together, and all the variables

-(2x^2+2x-144)=0

We get rid of parentheses

-2x^2-2x+144=0

a = -2; b = -2; c = +144;
Δ = b2-4ac
Δ = -22-4·(-2)·144
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*-2}=\frac{-32}{-4}
=+8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+34}{2*-2}=\frac{36}{-4}
=-9
$