x2+20x-144=0

Solution for x2+20x-144=0 equation:

x2+20x-144=0

We add all the numbers together, and all the variables

x^2+20x-144=0

a = 1; b = 20; c = -144;
Δ = b2-4ac
Δ = 202-4·1·(-144)
Δ = 976
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:

$\sqrt{\Delta}=\sqrt{976}=\sqrt{16*61}=\sqrt{16}*\sqrt{61}=4\sqrt{61}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-4\sqrt{61}}{2*1}=\frac{-20-4\sqrt{61}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+4\sqrt{61}}{2*1}=\frac{-20+4\sqrt{61}}{2}
$