80+4x-4x^2=4x^2-20x

Solution for 80+4x-4x^2=4x^2-20x equation:

80+4x-4x^2=4x^2-20x

We move all terms to the left:

80+4x-4x^2-(4x^2-20x)=0

We get rid of parentheses

-4x^2-4x^2+4x+20x+80=0

We add all the numbers together, and all the variables

-8x^2+24x+80=0

a = -8; b = 24; c = +80;
Δ = b2-4ac
Δ = 242-4·(-8)·80
Δ = 3136
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3136}=56$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-56}{2*-8}=\frac{-80}{-16}
=+5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+56}{2*-8}=\frac{32}{-16}
=-2
$