Y=5-8x+2x^2

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

=5-8Y+2Y^2

We move all terms to the left:

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

We get rid of parentheses

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

a = -2; b = 8; c = -5;
Δ = b2-4ac
Δ = 82-4·(-2)·(-5)
Δ = 24
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:

$\sqrt{\Delta}=\sqrt{24}=\sqrt{4*6}=\sqrt{4}*\sqrt{6}=2\sqrt{6}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{6}}{2*-2}=\frac{-8-2\sqrt{6}}{-4}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{6}}{2*-2}=\frac{-8+2\sqrt{6}}{-4}
$