x*x+4=768

Solution for x*x+4=768 equation:

x*x+4=768

We move all terms to the left:

x*x+4-(768)=0

We add all the numbers together, and all the variables

x*x-764=0

Wy multiply elements

x^2-764=0

a = 1; b = 0; c = -764;
Δ = b2-4ac
Δ = 02-4·1·(-764)
Δ = 3056
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:

$\sqrt{\Delta}=\sqrt{3056}=\sqrt{16*191}=\sqrt{16}*\sqrt{191}=4\sqrt{191}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{191}}{2*1}=\frac{0-4\sqrt{191}}{2}
=-\frac{4\sqrt{191}}{2}
=-2\sqrt{191}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{191}}{2*1}=\frac{0+4\sqrt{191}}{2}
=\frac{4\sqrt{191}}{2}
=2\sqrt{191}
$