(6x-7)(3x+16)=180

Solution for (6x-7)(3x+16)=180 equation:

(6x-7)(3x+16)=180

We move all terms to the left:

(6x-7)(3x+16)-(180)=0

We multiply parentheses ..

(+18x^2+96x-21x-112)-180=0

We get rid of parentheses

18x^2+96x-21x-112-180=0

We add all the numbers together, and all the variables

18x^2+75x-292=0

a = 18; b = 75; c = -292;
Δ = b2-4ac
Δ = 752-4·18·(-292)
Δ = 26649
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:

$\sqrt{\Delta}=\sqrt{26649}=\sqrt{81*329}=\sqrt{81}*\sqrt{329}=9\sqrt{329}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(75)-9\sqrt{329}}{2*18}=\frac{-75-9\sqrt{329}}{36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(75)+9\sqrt{329}}{2*18}=\frac{-75+9\sqrt{329}}{36}
$