(5x+8)(7x-16)=180

Solution for (5x+8)(7x-16)=180 equation:

(5x+8)(7x-16)=180

We move all terms to the left:

(5x+8)(7x-16)-(180)=0

We multiply parentheses ..

(+35x^2-80x+56x-128)-180=0

We get rid of parentheses

35x^2-80x+56x-128-180=0

We add all the numbers together, and all the variables

35x^2-24x-308=0

a = 35; b = -24; c = -308;
Δ = b2-4ac
Δ = -242-4·35·(-308)
Δ = 43696
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:

$\sqrt{\Delta}=\sqrt{43696}=\sqrt{16*2731}=\sqrt{16}*\sqrt{2731}=4\sqrt{2731}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-4\sqrt{2731}}{2*35}=\frac{24-4\sqrt{2731}}{70}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+4\sqrt{2731}}{2*35}=\frac{24+4\sqrt{2731}}{70}
$