0=2x2+8x-144

Solution for 0=2x2+8x-144 equation:

0=2x^2+8x-144

We move all terms to the left:

0-(2x^2+8x-144)=0

We add all the numbers together, and all the variables

-(2x^2+8x-144)=0

We get rid of parentheses

-2x^2-8x+144=0

a = -2; b = -8; c = +144;
Δ = b2-4ac
Δ = -82-4·(-2)·144
Δ = 1216
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:

$\sqrt{\Delta}=\sqrt{1216}=\sqrt{64*19}=\sqrt{64}*\sqrt{19}=8\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-8\sqrt{19}}{2*-2}=\frac{8-8\sqrt{19}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+8\sqrt{19}}{2*-2}=\frac{8+8\sqrt{19}}{-4}
$