s^2-6s=3

Solution for s^2-6s=3 equation:

s^2-6s=3

We move all terms to the left:

s^2-6s-(3)=0

a = 1; b = -6; c = -3;
Δ = b2-4ac
Δ = -62-4·1·(-3)
Δ = 48
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{48}=\sqrt{16*3}=\sqrt{16}*\sqrt{3}=4\sqrt{3}$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-4\sqrt{3}}{2*1}=\frac{6-4\sqrt{3}}{2}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+4\sqrt{3}}{2*1}=\frac{6+4\sqrt{3}}{2}
$