(7x-8)(4x+19)=180

Solution for (7x-8)(4x+19)=180 equation:

(7x-8)(4x+19)=180

We move all terms to the left:

(7x-8)(4x+19)-(180)=0

We multiply parentheses ..

(+28x^2+133x-32x-152)-180=0

We get rid of parentheses

28x^2+133x-32x-152-180=0

We add all the numbers together, and all the variables

28x^2+101x-332=0

a = 28; b = 101; c = -332;
Δ = b2-4ac
Δ = 1012-4·28·(-332)
Δ = 47385
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:

$\sqrt{\Delta}=\sqrt{47385}=\sqrt{729*65}=\sqrt{729}*\sqrt{65}=27\sqrt{65}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(101)-27\sqrt{65}}{2*28}=\frac{-101-27\sqrt{65}}{56}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(101)+27\sqrt{65}}{2*28}=\frac{-101+27\sqrt{65}}{56}
$