Y=10+8x-2x^2

Solution for Y=10+8x-2x^2 equation:

=10+8Y-2Y^2

We move all terms to the left:

-(10+8Y-2Y^2)=0

We get rid of parentheses

2Y^2-8Y-10=0

a = 2; b = -8; c = -10;
Δ = b2-4ac
Δ = -82-4·2·(-10)
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-12}{2*2}=\frac{-4}{4}
=-1
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+12}{2*2}=\frac{20}{4}
=5
$