Y+18=8x^2-4x

Solution for Y+18=8x^2-4x equation:

+18=8Y^2-4Y

We move all terms to the left:

+18-(8Y^2-4Y)=0

We get rid of parentheses

-8Y^2+4Y+18=0

a = -8; b = 4; c = +18;
Δ = b2-4ac
Δ = 42-4·(-8)·18
Δ = 592
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:

$\sqrt{\Delta}=\sqrt{592}=\sqrt{16*37}=\sqrt{16}*\sqrt{37}=4\sqrt{37}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{37}}{2*-8}=\frac{-4-4\sqrt{37}}{-16}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{37}}{2*-8}=\frac{-4+4\sqrt{37}}{-16}
$