Y=5x^2+80x+140

Solution for Y=5x^2+80x+140 equation:

=5Y^2+80Y+140

We move all terms to the left:

-(5Y^2+80Y+140)=0

We get rid of parentheses

-5Y^2-80Y-140=0

a = -5; b = -80; c = -140;
Δ = b2-4ac
Δ = -802-4·(-5)·(-140)
Δ = 3600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3600}=60$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-80)-60}{2*-5}=\frac{20}{-10}
=-2
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-80)+60}{2*-5}=\frac{140}{-10}
=-14
$