x^2-10x-3=5

Solution for x^2-10x-3=5 equation:

x^2-10x-3=5

We move all terms to the left:

x^2-10x-3-(5)=0

We add all the numbers together, and all the variables

x^2-10x-8=0

a = 1; b = -10; c = -8;
Δ = b2-4ac
Δ = -102-4·1·(-8)
Δ = 132
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:

$\sqrt{\Delta}=\sqrt{132}=\sqrt{4*33}=\sqrt{4}*\sqrt{33}=2\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{33}}{2*1}=\frac{10-2\sqrt{33}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{33}}{2*1}=\frac{10+2\sqrt{33}}{2}
$