468=384+80x+4x^2

Solution for 468=384+80x+4x^2 equation:

468=384+80x+4x^2

We move all terms to the left:

468-(384+80x+4x^2)=0

We get rid of parentheses

-4x^2-80x-384+468=0

We add all the numbers together, and all the variables

-4x^2-80x+84=0

a = -4; b = -80; c = +84;
Δ = b2-4ac
Δ = -802-4·(-4)·84
Δ = 7744
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{7744}=88$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-80)-88}{2*-4}=\frac{-8}{-8}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-80)+88}{2*-4}=\frac{168}{-8}
=-21
$