0=x^2+38x-144

Solution for 0=x^2+38x-144 equation:

0=x^2+38x-144

We move all terms to the left:

0-(x^2+38x-144)=0

We add all the numbers together, and all the variables

-(x^2+38x-144)=0

We get rid of parentheses

-x^2-38x+144=0

We add all the numbers together, and all the variables

-1x^2-38x+144=0

a = -1; b = -38; c = +144;
Δ = b2-4ac
Δ = -382-4·(-1)·144
Δ = 2020
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:

$\sqrt{\Delta}=\sqrt{2020}=\sqrt{4*505}=\sqrt{4}*\sqrt{505}=2\sqrt{505}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-38)-2\sqrt{505}}{2*-1}=\frac{38-2\sqrt{505}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-38)+2\sqrt{505}}{2*-1}=\frac{38+2\sqrt{505}}{-2}
$