(8b+6)(9b-7)=180

Solution for (8b+6)(9b-7)=180 equation:

(8b+6)(9b-7)=180

We move all terms to the left:

(8b+6)(9b-7)-(180)=0

We multiply parentheses ..

(+72b^2-56b+54b-42)-180=0

We get rid of parentheses

72b^2-56b+54b-42-180=0

We add all the numbers together, and all the variables

72b^2-2b-222=0

a = 72; b = -2; c = -222;
Δ = b2-4ac
Δ = -22-4·72·(-222)
Δ = 63940
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{63940}=\sqrt{4*15985}=\sqrt{4}*\sqrt{15985}=2\sqrt{15985}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{15985}}{2*72}=\frac{2-2\sqrt{15985}}{144}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{15985}}{2*72}=\frac{2+2\sqrt{15985}}{144}
$