Y=4x^2+3x-115

Solution for Y=4x^2+3x-115 equation:

=4Y^2+3Y-115

We move all terms to the left:

-(4Y^2+3Y-115)=0

We get rid of parentheses

-4Y^2-3Y+115=0

a = -4; b = -3; c = +115;
Δ = b2-4ac
Δ = -32-4·(-4)·115
Δ = 1849
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1849}=43$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-43}{2*-4}=\frac{-40}{-8}
=+5
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+43}{2*-4}=\frac{46}{-8}
=-5+3/4
$