42=4x^2

Solution for 42=4x^2 equation:

42=4x^2

We move all terms to the left:

42-(4x^2)=0

a = -4; b = 0; c = +42;
Δ = b2-4ac
Δ = 02-4·(-4)·42
Δ = 672
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:

$\sqrt{\Delta}=\sqrt{672}=\sqrt{16*42}=\sqrt{16}*\sqrt{42}=4\sqrt{42}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{42}}{2*-4}=\frac{0-4\sqrt{42}}{-8}
=-\frac{4\sqrt{42}}{-8}
=-\frac{\sqrt{42}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{42}}{2*-4}=\frac{0+4\sqrt{42}}{-8}
=\frac{4\sqrt{42}}{-8}
=\frac{\sqrt{42}}{-2}
$