180=3y(5y-22)

Solution for 180=3y(5y-22) equation:

180=3y(5y-22)

We move all terms to the left:

180-(3y(5y-22))=0


We calculate terms in parentheses: -(3y(5y-22)), so:

3y(5y-22)

We multiply parentheses

15y^2-66y

Back to the equation:

-(15y^2-66y)


We get rid of parentheses

-15y^2+66y+180=0

a = -15; b = 66; c = +180;
Δ = b2-4ac
Δ = 662-4·(-15)·180
Δ = 15156
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:

$\sqrt{\Delta}=\sqrt{15156}=\sqrt{36*421}=\sqrt{36}*\sqrt{421}=6\sqrt{421}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(66)-6\sqrt{421}}{2*-15}=\frac{-66-6\sqrt{421}}{-30}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(66)+6\sqrt{421}}{2*-15}=\frac{-66+6\sqrt{421}}{-30}
$