-4x^2+408=20-8x

Solution for -4x^2+408=20-8x equation:

-4x^2+408=20-8x

We move all terms to the left:

-4x^2+408-(20-8x)=0

We add all the numbers together, and all the variables

-4x^2-(-8x+20)+408=0

We get rid of parentheses

-4x^2+8x-20+408=0

We add all the numbers together, and all the variables

-4x^2+8x+388=0

a = -4; b = 8; c = +388;
Δ = b2-4ac
Δ = 82-4·(-4)·388
Δ = 6272
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{6272}=\sqrt{3136*2}=\sqrt{3136}*\sqrt{2}=56\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-56\sqrt{2}}{2*-4}=\frac{-8-56\sqrt{2}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+56\sqrt{2}}{2*-4}=\frac{-8+56\sqrt{2}}{-8}
$