Y=2x^2+15x+3

Solution for Y=2x^2+15x+3 equation:

=2Y^2+15Y+3

We move all terms to the left:

-(2Y^2+15Y+3)=0

We get rid of parentheses

-2Y^2-15Y-3=0

a = -2; b = -15; c = -3;
Δ = b2-4ac
Δ = -152-4·(-2)·(-3)
Δ = 201
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-\sqrt{201}}{2*-2}=\frac{15-\sqrt{201}}{-4}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+\sqrt{201}}{2*-2}=\frac{15+\sqrt{201}}{-4}
$