83=u^2+3

Solution for 83=u^2+3 equation:

83=u^2+3

We move all terms to the left:

83-(u^2+3)=0

We get rid of parentheses

-u^2-3+83=0

We add all the numbers together, and all the variables

-1u^2+80=0

a = -1; b = 0; c = +80;
Δ = b2-4ac
Δ = 02-4·(-1)·80
Δ = 320
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{320}=\sqrt{64*5}=\sqrt{64}*\sqrt{5}=8\sqrt{5}$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{5}}{2*-1}=\frac{0-8\sqrt{5}}{-2}
=-\frac{8\sqrt{5}}{-2}
=-\frac{4\sqrt{5}}{-1}
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{5}}{2*-1}=\frac{0+8\sqrt{5}}{-2}
=\frac{8\sqrt{5}}{-2}
=\frac{4\sqrt{5}}{-1}
$