(8x-14)(2x+4)=180

Solution for (8x-14)(2x+4)=180 equation:

(8x-14)(2x+4)=180

We move all terms to the left:

(8x-14)(2x+4)-(180)=0

We multiply parentheses ..

(+16x^2+32x-28x-56)-180=0

We get rid of parentheses

16x^2+32x-28x-56-180=0

We add all the numbers together, and all the variables

16x^2+4x-236=0

a = 16; b = 4; c = -236;
Δ = b2-4ac
Δ = 42-4·16·(-236)
Δ = 15120
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:

$\sqrt{\Delta}=\sqrt{15120}=\sqrt{144*105}=\sqrt{144}*\sqrt{105}=12\sqrt{105}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-12\sqrt{105}}{2*16}=\frac{-4-12\sqrt{105}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+12\sqrt{105}}{2*16}=\frac{-4+12\sqrt{105}}{32}
$