(8+2x)(16+2x)=468

Solution for (8+2x)(16+2x)=468 equation:

(8+2x)(16+2x)=468

We move all terms to the left:

(8+2x)(16+2x)-(468)=0

We add all the numbers together, and all the variables

(2x+8)(2x+16)-468=0

We multiply parentheses ..

(+4x^2+32x+16x+128)-468=0

We get rid of parentheses

4x^2+32x+16x+128-468=0

We add all the numbers together, and all the variables

4x^2+48x-340=0

a = 4; b = 48; c = -340;
Δ = b2-4ac
Δ = 482-4·4·(-340)
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{-(48)-88}{2*4}=\frac{-136}{8}
=-17
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+88}{2*4}=\frac{40}{8}
=5
$