32=(x^2+2)

Solution for 32=(x^2+2) equation:

32=(x^2+2)

We move all terms to the left:

32-((x^2+2))=0


We calculate terms in parentheses: -((x^2+2)), so:

(x^2+2)

We get rid of parentheses

x^2+2

Back to the equation:

-(x^2+2)


We get rid of parentheses

-x^2-2+32=0

We add all the numbers together, and all the variables

-1x^2+30=0

a = -1; b = 0; c = +30;
Δ = b2-4ac
Δ = 02-4·(-1)·30
Δ = 120
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{120}=\sqrt{4*30}=\sqrt{4}*\sqrt{30}=2\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{30}}{2*-1}=\frac{0-2\sqrt{30}}{-2}
=-\frac{2\sqrt{30}}{-2}
=-\frac{\sqrt{30}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{30}}{2*-1}=\frac{0+2\sqrt{30}}{-2}
=\frac{2\sqrt{30}}{-2}
=\frac{\sqrt{30}}{-1}
$