(x+8)(x-5)=420

Solution for (x+8)(x-5)=420 equation:

(x+8)(x-5)=420

We move all terms to the left:

(x+8)(x-5)-(420)=0

We multiply parentheses ..

(+x^2-5x+8x-40)-420=0

We get rid of parentheses

x^2-5x+8x-40-420=0

We add all the numbers together, and all the variables

x^2+3x-460=0

a = 1; b = 3; c = -460;
Δ = b2-4ac
Δ = 32-4·1·(-460)
Δ = 1849
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1849}=43$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-43}{2*1}=\frac{-46}{2}
=-23
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+43}{2*1}=\frac{40}{2}
=20
$