Y=2x^2-x-8

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

=2Y^2-Y-8

We move all terms to the left:

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

We get rid of parentheses

-2Y^2+Y+8=0

a = -2; b = 1; c = +8;
Δ = b2-4ac
Δ = 12-4·(-2)·8
Δ = 65
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{-(1)-\sqrt{65}}{2*-2}=\frac{-1-\sqrt{65}}{-4}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{65}}{2*-2}=\frac{-1+\sqrt{65}}{-4}
$