11=12^2-x^2/4

Solution for 11=12^2-x^2/4 equation:

11=12^2-x^2/4

We move all terms to the left:

11-(12^2-x^2/4)=0

We get rid of parentheses

x^2/4+11-12^2=0

We multiply all the terms by the denominator


x^2+11*4-12^2*4=0

We add all the numbers together, and all the variables

x^2-532=0

a = 1; b = 0; c = -532;
Δ = b2-4ac
Δ = 02-4·1·(-532)
Δ = 2128
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:

$\sqrt{\Delta}=\sqrt{2128}=\sqrt{16*133}=\sqrt{16}*\sqrt{133}=4\sqrt{133}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{133}}{2*1}=\frac{0-4\sqrt{133}}{2}
=-\frac{4\sqrt{133}}{2}
=-2\sqrt{133}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{133}}{2*1}=\frac{0+4\sqrt{133}}{2}
=\frac{4\sqrt{133}}{2}
=2\sqrt{133}
$