Y=4x^2-17x-15

Solution for Y=4x^2-17x-15 equation:

=4Y^2-17Y-15

We move all terms to the left:

-(4Y^2-17Y-15)=0

We get rid of parentheses

-4Y^2+17Y+15=0

a = -4; b = 17; c = +15;
Δ = b2-4ac
Δ = 172-4·(-4)·15
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-23}{2*-4}=\frac{-40}{-8}
=+5
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+23}{2*-4}=\frac{6}{-8}
=-3/4
$