(5x+32)(7x+8)=180

Solution for (5x+32)(7x+8)=180 equation:

(5x+32)(7x+8)=180

We move all terms to the left:

(5x+32)(7x+8)-(180)=0

We multiply parentheses ..

(+35x^2+40x+224x+256)-180=0

We get rid of parentheses

35x^2+40x+224x+256-180=0

We add all the numbers together, and all the variables

35x^2+264x+76=0

a = 35; b = 264; c = +76;
Δ = b2-4ac
Δ = 2642-4·35·76
Δ = 59056
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:

$\sqrt{\Delta}=\sqrt{59056}=\sqrt{16*3691}=\sqrt{16}*\sqrt{3691}=4\sqrt{3691}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(264)-4\sqrt{3691}}{2*35}=\frac{-264-4\sqrt{3691}}{70}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(264)+4\sqrt{3691}}{2*35}=\frac{-264+4\sqrt{3691}}{70}
$