x^2-6x=79

Solution for x^2-6x=79 equation:

x^2-6x=79

We move all terms to the left:

x^2-6x-(79)=0

a = 1; b = -6; c = -79;
Δ = b2-4ac
Δ = -62-4·1·(-79)
Δ = 352
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:

$\sqrt{\Delta}=\sqrt{352}=\sqrt{16*22}=\sqrt{16}*\sqrt{22}=4\sqrt{22}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-4\sqrt{22}}{2*1}=\frac{6-4\sqrt{22}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+4\sqrt{22}}{2*1}=\frac{6+4\sqrt{22}}{2}
$