x(x-1)=34

Solution for x(x-1)=34 equation:

x(x-1)=34

We move all terms to the left:

x(x-1)-(34)=0

We multiply parentheses

x^2-1x-34=0

a = 1; b = -1; c = -34;
Δ = b2-4ac
Δ = -12-4·1·(-34)
Δ = 137
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-\sqrt{137}}{2*1}=\frac{1-\sqrt{137}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{137}}{2*1}=\frac{1+\sqrt{137}}{2}
$