Y=5x2+10x-40

Solution for Y=5x2+10x-40 equation:

=5Y^2+10Y-40

We move all terms to the left:

-(5Y^2+10Y-40)=0

We get rid of parentheses

-5Y^2-10Y+40=0

a = -5; b = -10; c = +40;
Δ = b2-4ac
Δ = -102-4·(-5)·40
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-30}{2*-5}=\frac{-20}{-10}
=+2
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+30}{2*-5}=\frac{40}{-10}
=-4
$