(x+17)(4x-7)=180

Solution for (x+17)(4x-7)=180 equation:

(x+17)(4x-7)=180

We move all terms to the left:

(x+17)(4x-7)-(180)=0

We multiply parentheses ..

(+4x^2-7x+68x-119)-180=0

We get rid of parentheses

4x^2-7x+68x-119-180=0

We add all the numbers together, and all the variables

4x^2+61x-299=0

a = 4; b = 61; c = -299;
Δ = b2-4ac
Δ = 612-4·4·(-299)
Δ = 8505
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:

$\sqrt{\Delta}=\sqrt{8505}=\sqrt{81*105}=\sqrt{81}*\sqrt{105}=9\sqrt{105}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(61)-9\sqrt{105}}{2*4}=\frac{-61-9\sqrt{105}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(61)+9\sqrt{105}}{2*4}=\frac{-61+9\sqrt{105}}{8}
$