Y=10x^2+80x+60

Solution for Y=10x^2+80x+60 equation:

=10Y^2+80Y+60

We move all terms to the left:

-(10Y^2+80Y+60)=0

We get rid of parentheses

-10Y^2-80Y-60=0

a = -10; b = -80; c = -60;
Δ = b2-4ac
Δ = -802-4·(-10)·(-60)
Δ = 4000
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:

$\sqrt{\Delta}=\sqrt{4000}=\sqrt{400*10}=\sqrt{400}*\sqrt{10}=20\sqrt{10}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-80)-20\sqrt{10}}{2*-10}=\frac{80-20\sqrt{10}}{-20}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-80)+20\sqrt{10}}{2*-10}=\frac{80+20\sqrt{10}}{-20}
$