(7x+8)(-2+22x)=180

Solution for (7x+8)(-2+22x)=180 equation:

(7x+8)(-2+22x)=180

We move all terms to the left:

(7x+8)(-2+22x)-(180)=0

We add all the numbers together, and all the variables

(7x+8)(22x-2)-180=0

We multiply parentheses ..

(+154x^2-14x+176x-16)-180=0

We get rid of parentheses

154x^2-14x+176x-16-180=0

We add all the numbers together, and all the variables

154x^2+162x-196=0

a = 154; b = 162; c = -196;
Δ = b2-4ac
Δ = 1622-4·154·(-196)
Δ = 146980
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:

$\sqrt{\Delta}=\sqrt{146980}=\sqrt{4*36745}=\sqrt{4}*\sqrt{36745}=2\sqrt{36745}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(162)-2\sqrt{36745}}{2*154}=\frac{-162-2\sqrt{36745}}{308}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(162)+2\sqrt{36745}}{2*154}=\frac{-162+2\sqrt{36745}}{308}
$