40(x+1)-2x(x+1)=0

Solution for 40(x+1)-2x(x+1)=0 equation:

40(x+1)-2x(x+1)=0

We multiply parentheses

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

We add all the numbers together, and all the variables

-2x^2+38x+40=0

a = -2; b = 38; c = +40;
Δ = b2-4ac
Δ = 382-4·(-2)·40
Δ = 1764
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1764}=42$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(38)-42}{2*-2}=\frac{-80}{-4}
=+20
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(38)+42}{2*-2}=\frac{4}{-4}
=-1
$