(6x-8)(5x+14)=180

Solution for (6x-8)(5x+14)=180 equation:

(6x-8)(5x+14)=180

We move all terms to the left:

(6x-8)(5x+14)-(180)=0

We multiply parentheses ..

(+30x^2+84x-40x-112)-180=0

We get rid of parentheses

30x^2+84x-40x-112-180=0

We add all the numbers together, and all the variables

30x^2+44x-292=0

a = 30; b = 44; c = -292;
Δ = b2-4ac
Δ = 442-4·30·(-292)
Δ = 36976
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:

$\sqrt{\Delta}=\sqrt{36976}=\sqrt{16*2311}=\sqrt{16}*\sqrt{2311}=4\sqrt{2311}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(44)-4\sqrt{2311}}{2*30}=\frac{-44-4\sqrt{2311}}{60}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(44)+4\sqrt{2311}}{2*30}=\frac{-44+4\sqrt{2311}}{60}
$