(4x+16)(5x+2)=180

Solution for (4x+16)(5x+2)=180 equation:

(4x+16)(5x+2)=180

We move all terms to the left:

(4x+16)(5x+2)-(180)=0

We multiply parentheses ..

(+20x^2+8x+80x+32)-180=0

We get rid of parentheses

20x^2+8x+80x+32-180=0

We add all the numbers together, and all the variables

20x^2+88x-148=0

a = 20; b = 88; c = -148;
Δ = b2-4ac
Δ = 882-4·20·(-148)
Δ = 19584
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:

$\sqrt{\Delta}=\sqrt{19584}=\sqrt{576*34}=\sqrt{576}*\sqrt{34}=24\sqrt{34}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(88)-24\sqrt{34}}{2*20}=\frac{-88-24\sqrt{34}}{40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(88)+24\sqrt{34}}{2*20}=\frac{-88+24\sqrt{34}}{40}
$