X2-6x=3

Solution for X2-6x=3 equation:

X2-6X=3

We move all terms to the left:

X2-6X-(3)=0

We add all the numbers together, and all the variables

X^2-6X-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:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

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