Y=5x^2+10x-45

Solution for Y=5x^2+10x-45 equation:

=5Y^2+10Y-45

We move all terms to the left:

-(5Y^2+10Y-45)=0

We get rid of parentheses

-5Y^2-10Y+45=0

a = -5; b = -10; c = +45;
Δ = b2-4ac
Δ = -102-4·(-5)·45
Δ = 1000
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:

$\sqrt{\Delta}=\sqrt{1000}=\sqrt{100*10}=\sqrt{100}*\sqrt{10}=10\sqrt{10}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-10\sqrt{10}}{2*-5}=\frac{10-10\sqrt{10}}{-10}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+10\sqrt{10}}{2*-5}=\frac{10+10\sqrt{10}}{-10}
$