Y=4x^2+7x-8

Solution for Y=4x^2+7x-8 equation:

=4Y^2+7Y-8

We move all terms to the left:

-(4Y^2+7Y-8)=0

We get rid of parentheses

-4Y^2-7Y+8=0

a = -4; b = -7; c = +8;
Δ = b2-4ac
Δ = -72-4·(-4)·8
Δ = 177
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{-(-7)-\sqrt{177}}{2*-4}=\frac{7-\sqrt{177}}{-8}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{177}}{2*-4}=\frac{7+\sqrt{177}}{-8}
$