Y=4x^2-5x-51

Solution for Y=4x^2-5x-51 equation:

=4Y^2-5Y-51

We move all terms to the left:

-(4Y^2-5Y-51)=0

We get rid of parentheses

-4Y^2+5Y+51=0

a = -4; b = 5; c = +51;
Δ = b2-4ac
Δ = 52-4·(-4)·51
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-29}{2*-4}=\frac{-34}{-8}
=4+1/4
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+29}{2*-4}=\frac{24}{-8}
=-3
$