x(x-6)=34

Solution for x(x-6)=34 equation:

x(x-6)=34

We move all terms to the left:

x(x-6)-(34)=0

We multiply parentheses

x^2-6x-34=0

a = 1; b = -6; c = -34;
Δ = b2-4ac
Δ = -62-4·1·(-34)
Δ = 172
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:

$\sqrt{\Delta}=\sqrt{172}=\sqrt{4*43}=\sqrt{4}*\sqrt{43}=2\sqrt{43}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{43}}{2*1}=\frac{6-2\sqrt{43}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{43}}{2*1}=\frac{6+2\sqrt{43}}{2}
$