42=u^2+2

Solution for 42=u^2+2 equation:

42=u^2+2

We move all terms to the left:

42-(u^2+2)=0

We get rid of parentheses

-u^2-2+42=0

We add all the numbers together, and all the variables

-1u^2+40=0

a = -1; b = 0; c = +40;
Δ = b2-4ac
Δ = 02-4·(-1)·40
Δ = 160
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{160}=\sqrt{16*10}=\sqrt{16}*\sqrt{10}=4\sqrt{10}$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{10}}{2*-1}=\frac{0-4\sqrt{10}}{-2}
=-\frac{4\sqrt{10}}{-2}
=-\frac{2\sqrt{10}}{-1}
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{10}}{2*-1}=\frac{0+4\sqrt{10}}{-2}
=\frac{4\sqrt{10}}{-2}
=\frac{2\sqrt{10}}{-1}
$