(x+40)(x-10)=0

Solution for (x+40)(x-10)=0 equation:

(x+40)(x-10)=0

We multiply parentheses ..

(+x^2-10x+40x-400)=0

We get rid of parentheses

x^2-10x+40x-400=0

We add all the numbers together, and all the variables

x^2+30x-400=0

a = 1; b = 30; c = -400;
Δ = b2-4ac
Δ = 302-4·1·(-400)
Δ = 2500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2500}=50$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-50}{2*1}=\frac{-80}{2}
=-40
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+50}{2*1}=\frac{20}{2}
=10
$