x(x-6)=68

Solution for x(x-6)=68 equation:

x(x-6)=68

We move all terms to the left:

x(x-6)-(68)=0

We multiply parentheses

x^2-6x-68=0

a = 1; b = -6; c = -68;
Δ = b2-4ac
Δ = -62-4·1·(-68)
Δ = 308
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:

$\sqrt{\Delta}=\sqrt{308}=\sqrt{4*77}=\sqrt{4}*\sqrt{77}=2\sqrt{77}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{77}}{2*1}=\frac{6-2\sqrt{77}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{77}}{2*1}=\frac{6+2\sqrt{77}}{2}
$