(6y+40)(24y-10)=180

Solution for (6y+40)(24y-10)=180 equation:

(6y+40)(24y-10)=180

We move all terms to the left:

(6y+40)(24y-10)-(180)=0

We multiply parentheses ..

(+144y^2-60y+960y-400)-180=0

We get rid of parentheses

144y^2-60y+960y-400-180=0

We add all the numbers together, and all the variables

144y^2+900y-580=0

a = 144; b = 900; c = -580;
Δ = b2-4ac
Δ = 9002-4·144·(-580)
Δ = 1144080
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:

$\sqrt{\Delta}=\sqrt{1144080}=\sqrt{144*7945}=\sqrt{144}*\sqrt{7945}=12\sqrt{7945}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(900)-12\sqrt{7945}}{2*144}=\frac{-900-12\sqrt{7945}}{288}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(900)+12\sqrt{7945}}{2*144}=\frac{-900+12\sqrt{7945}}{288}
$