-42=-5u^2

Solution for -42=-5u^2 equation:

-42=-5u^2

We move all terms to the left:

-42-(-5u^2)=0

We get rid of parentheses

5u^2-42=0

a = 5; b = 0; c = -42;
Δ = b2-4ac
Δ = 02-4·5·(-42)
Δ = 840
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:

$\sqrt{\Delta}=\sqrt{840}=\sqrt{4*210}=\sqrt{4}*\sqrt{210}=2\sqrt{210}$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{210}}{2*5}=\frac{0-2\sqrt{210}}{10}
=-\frac{2\sqrt{210}}{10}
=-\frac{\sqrt{210}}{5}
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{210}}{2*5}=\frac{0+2\sqrt{210}}{10}
=\frac{2\sqrt{210}}{10}
=\frac{\sqrt{210}}{5}
$