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

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

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

We move all terms to the left:

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

We multiply parentheses ..

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


We calculate terms in parentheses: -((+x^2-5x+8x-40)), so:

(+x^2-5x+8x-40)

We get rid of parentheses

x^2-5x+8x-40

We add all the numbers together, and all the variables

x^2+3x-40

Back to the equation:

-(x^2+3x-40)


We get rid of parentheses

-x^2-3x+40+420=0

We add all the numbers together, and all the variables

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