Y=4x2+16x+15

Solution for Y=4x2+16x+15 equation:

=4Y^2+16Y+15

We move all terms to the left:

-(4Y^2+16Y+15)=0

We get rid of parentheses

-4Y^2-16Y-15=0

a = -4; b = -16; c = -15;
Δ = b2-4ac
Δ = -162-4·(-4)·(-15)
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-4}{2*-4}=\frac{12}{-8}
=-1+1/2
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+4}{2*-4}=\frac{20}{-8}
=-2+1/2
$