x^2-22x=3

Solution for x^2-22x=3 equation:

x^2-22x=3

We move all terms to the left:

x^2-22x-(3)=0

a = 1; b = -22; c = -3;
Δ = b2-4ac
Δ = -222-4·1·(-3)
Δ = 496
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:

$\sqrt{\Delta}=\sqrt{496}=\sqrt{16*31}=\sqrt{16}*\sqrt{31}=4\sqrt{31}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-4\sqrt{31}}{2*1}=\frac{22-4\sqrt{31}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+4\sqrt{31}}{2*1}=\frac{22+4\sqrt{31}}{2}
$