Y=4x^2-32+10

Solution for Y=4x^2-32+10 equation:

=4Y^2-32+10

We move all terms to the left:

-(4Y^2-32+10)=0

We get rid of parentheses

-4Y^2+32-10=0

We add all the numbers together, and all the variables

-4Y^2+22=0

a = -4; b = 0; c = +22;
Δ = b2-4ac
Δ = 02-4·(-4)·22
Δ = 352
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:

$\sqrt{\Delta}=\sqrt{352}=\sqrt{16*22}=\sqrt{16}*\sqrt{22}=4\sqrt{22}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{22}}{2*-4}=\frac{0-4\sqrt{22}}{-8}
=-\frac{4\sqrt{22}}{-8}
=-\frac{\sqrt{22}}{-2}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{22}}{2*-4}=\frac{0+4\sqrt{22}}{-8}
=\frac{4\sqrt{22}}{-8}
=\frac{\sqrt{22}}{-2}
$