(7n+2)(9n-8)=180

Solution for (7n+2)(9n-8)=180 equation:

(7n+2)(9n-8)=180

We move all terms to the left:

(7n+2)(9n-8)-(180)=0

We multiply parentheses ..

(+63n^2-56n+18n-16)-180=0

We get rid of parentheses

63n^2-56n+18n-16-180=0

We add all the numbers together, and all the variables

63n^2-38n-196=0

a = 63; b = -38; c = -196;
Δ = b2-4ac
Δ = -382-4·63·(-196)
Δ = 50836
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{50836}=\sqrt{4*12709}=\sqrt{4}*\sqrt{12709}=2\sqrt{12709}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-38)-2\sqrt{12709}}{2*63}=\frac{38-2\sqrt{12709}}{126}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-38)+2\sqrt{12709}}{2*63}=\frac{38+2\sqrt{12709}}{126}
$