Y=8x^2-5x-4

Solution for Y=8x^2-5x-4 equation:

=8Y^2-5Y-4

We move all terms to the left:

-(8Y^2-5Y-4)=0

We get rid of parentheses

-8Y^2+5Y+4=0

a = -8; b = 5; c = +4;
Δ = b2-4ac
Δ = 52-4·(-8)·4
Δ = 153
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{153}=\sqrt{9*17}=\sqrt{9}*\sqrt{17}=3\sqrt{17}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-3\sqrt{17}}{2*-8}=\frac{-5-3\sqrt{17}}{-16}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+3\sqrt{17}}{2*-8}=\frac{-5+3\sqrt{17}}{-16}
$