Y=x^2+2^2-48

Solution for Y=x^2+2^2-48 equation:

=Y^2+2^2-48

We move all terms to the left:

-(Y^2+2^2-48)=0

We get rid of parentheses

-Y^2+48-2^2=0

We add all the numbers together, and all the variables

-1Y^2+44=0

a = -1; b = 0; c = +44;
Δ = b2-4ac
Δ = 02-4·(-1)·44
Δ = 176
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:

$\sqrt{\Delta}=\sqrt{176}=\sqrt{16*11}=\sqrt{16}*\sqrt{11}=4\sqrt{11}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{11}}{2*-1}=\frac{0-4\sqrt{11}}{-2}
=-\frac{4\sqrt{11}}{-2}
=-\frac{2\sqrt{11}}{-1}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{11}}{2*-1}=\frac{0+4\sqrt{11}}{-2}
=\frac{4\sqrt{11}}{-2}
=\frac{2\sqrt{11}}{-1}
$