(4x-14)(x+8)=180

Solution for (4x-14)(x+8)=180 equation:

(4x-14)(x+8)=180

We move all terms to the left:

(4x-14)(x+8)-(180)=0

We multiply parentheses ..

(+4x^2+32x-14x-112)-180=0

We get rid of parentheses

4x^2+32x-14x-112-180=0

We add all the numbers together, and all the variables

4x^2+18x-292=0

a = 4; b = 18; c = -292;
Δ = b2-4ac
Δ = 182-4·4·(-292)
Δ = 4996
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:

$\sqrt{\Delta}=\sqrt{4996}=\sqrt{4*1249}=\sqrt{4}*\sqrt{1249}=2\sqrt{1249}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-2\sqrt{1249}}{2*4}=\frac{-18-2\sqrt{1249}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+2\sqrt{1249}}{2*4}=\frac{-18+2\sqrt{1249}}{8}
$