(14x+4)(16x-4)=180

Solution for (14x+4)(16x-4)=180 equation:

(14x+4)(16x-4)=180

We move all terms to the left:

(14x+4)(16x-4)-(180)=0

We multiply parentheses ..

(+224x^2-56x+64x-16)-180=0

We get rid of parentheses

224x^2-56x+64x-16-180=0

We add all the numbers together, and all the variables

224x^2+8x-196=0

a = 224; b = 8; c = -196;
Δ = b2-4ac
Δ = 82-4·224·(-196)
Δ = 175680
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:

$\sqrt{\Delta}=\sqrt{175680}=\sqrt{576*305}=\sqrt{576}*\sqrt{305}=24\sqrt{305}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-24\sqrt{305}}{2*224}=\frac{-8-24\sqrt{305}}{448}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+24\sqrt{305}}{2*224}=\frac{-8+24\sqrt{305}}{448}
$