42=4x^2-10

Solution for 42=4x^2-10 equation:

42=4x^2-10

We move all terms to the left:

42-(4x^2-10)=0

We get rid of parentheses

-4x^2+10+42=0

We add all the numbers together, and all the variables

-4x^2+52=0

a = -4; b = 0; c = +52;
Δ = b2-4ac
Δ = 02-4·(-4)·52
Δ = 832
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:

$\sqrt{\Delta}=\sqrt{832}=\sqrt{64*13}=\sqrt{64}*\sqrt{13}=8\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{13}}{2*-4}=\frac{0-8\sqrt{13}}{-8}
=-\frac{8\sqrt{13}}{-8}
=-\frac{\sqrt{13}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{13}}{2*-4}=\frac{0+8\sqrt{13}}{-8}
=\frac{8\sqrt{13}}{-8}
=\frac{\sqrt{13}}{-1}
$