(x-40)(x+70)=0

Solution for (x-40)(x+70)=0 equation:

(x-40)(x+70)=0

We multiply parentheses ..

(+x^2+70x-40x-2800)=0

We get rid of parentheses

x^2+70x-40x-2800=0

We add all the numbers together, and all the variables

x^2+30x-2800=0

a = 1; b = 30; c = -2800;
Δ = b2-4ac
Δ = 302-4·1·(-2800)
Δ = 12100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{12100}=110$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-110}{2*1}=\frac{-140}{2}
=-70
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+110}{2*1}=\frac{80}{2}
=40
$