(4x2)=42

Solution for (4x2)=42 equation:

(4x^2)=42

We move all terms to the left:

(4x^2)-(42)=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}
$