(x+20)(x-5)=350

Solution for (x+20)(x-5)=350 equation:

(x+20)(x-5)=350

We move all terms to the left:

(x+20)(x-5)-(350)=0

We multiply parentheses ..

(+x^2-5x+20x-100)-350=0

We get rid of parentheses

x^2-5x+20x-100-350=0

We add all the numbers together, and all the variables

x^2+15x-450=0

a = 1; b = 15; c = -450;
Δ = b2-4ac
Δ = 152-4·1·(-450)
Δ = 2025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2025}=45$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-45}{2*1}=\frac{-60}{2}
=-30
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+45}{2*1}=\frac{30}{2}
=15
$