233=x^2-7

Solution for 233=x^2-7 equation:

233=x^2-7

We move all terms to the left:

233-(x^2-7)=0

We get rid of parentheses

-x^2+7+233=0

We add all the numbers together, and all the variables

-1x^2+240=0

a = -1; b = 0; c = +240;
Δ = b2-4ac
Δ = 02-4·(-1)·240
Δ = 960
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:

$\sqrt{\Delta}=\sqrt{960}=\sqrt{64*15}=\sqrt{64}*\sqrt{15}=8\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{15}}{2*-1}=\frac{0-8\sqrt{15}}{-2}
=-\frac{8\sqrt{15}}{-2}
=-\frac{4\sqrt{15}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{15}}{2*-1}=\frac{0+8\sqrt{15}}{-2}
=\frac{8\sqrt{15}}{-2}
=\frac{4\sqrt{15}}{-1}
$