(10+2x)(8+2x)=144

Solution for (10+2x)(8+2x)=144 equation:

(10+2x)(8+2x)=144

We move all terms to the left:

(10+2x)(8+2x)-(144)=0

We add all the numbers together, and all the variables

(2x+10)(2x+8)-144=0

We multiply parentheses ..

(+4x^2+16x+20x+80)-144=0

We get rid of parentheses

4x^2+16x+20x+80-144=0

We add all the numbers together, and all the variables

4x^2+36x-64=0

a = 4; b = 36; c = -64;
Δ = b2-4ac
Δ = 362-4·4·(-64)
Δ = 2320
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:

$\sqrt{\Delta}=\sqrt{2320}=\sqrt{16*145}=\sqrt{16}*\sqrt{145}=4\sqrt{145}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-4\sqrt{145}}{2*4}=\frac{-36-4\sqrt{145}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+4\sqrt{145}}{2*4}=\frac{-36+4\sqrt{145}}{8}
$