(16y-6)*(9y+5)=180

Solution for (16y-6)*(9y+5)=180 equation:

(16y-6)(9y+5)=180

We move all terms to the left:

(16y-6)(9y+5)-(180)=0

We multiply parentheses ..

(+144y^2+80y-54y-30)-180=0

We get rid of parentheses

144y^2+80y-54y-30-180=0

We add all the numbers together, and all the variables

144y^2+26y-210=0

a = 144; b = 26; c = -210;
Δ = b2-4ac
Δ = 262-4·144·(-210)
Δ = 121636
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{121636}=\sqrt{4*30409}=\sqrt{4}*\sqrt{30409}=2\sqrt{30409}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(26)-2\sqrt{30409}}{2*144}=\frac{-26-2\sqrt{30409}}{288}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(26)+2\sqrt{30409}}{2*144}=\frac{-26+2\sqrt{30409}}{288}
$