Y=5x^2+15x+10

Solution for Y=5x^2+15x+10 equation:

=5Y^2+15Y+10

We move all terms to the left:

-(5Y^2+15Y+10)=0

We get rid of parentheses

-5Y^2-15Y-10=0

a = -5; b = -15; c = -10;
Δ = b2-4ac
Δ = -152-4·(-5)·(-10)
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-5}{2*-5}=\frac{10}{-10}
=-1
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+5}{2*-5}=\frac{20}{-10}
=-2
$