67=x^2-42

Solution for 67=x^2-42 equation:

67=x^2-42

We move all terms to the left:

67-(x^2-42)=0

We get rid of parentheses

-x^2+42+67=0

We add all the numbers together, and all the variables

-1x^2+109=0

a = -1; b = 0; c = +109;
Δ = b2-4ac
Δ = 02-4·(-1)·109
Δ = 436
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:

$\sqrt{\Delta}=\sqrt{436}=\sqrt{4*109}=\sqrt{4}*\sqrt{109}=2\sqrt{109}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{109}}{2*-1}=\frac{0-2\sqrt{109}}{-2}
=-\frac{2\sqrt{109}}{-2}
=-\frac{\sqrt{109}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{109}}{2*-1}=\frac{0+2\sqrt{109}}{-2}
=\frac{2\sqrt{109}}{-2}
=\frac{\sqrt{109}}{-1}
$