x(2x-1)=100

Solution for x(2x-1)=100 equation:

x(2x-1)=100

We move all terms to the left:

x(2x-1)-(100)=0

We multiply parentheses

2x^2-1x-100=0

a = 2; b = -1; c = -100;
Δ = b2-4ac
Δ = -12-4·2·(-100)
Δ = 801
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:

$\sqrt{\Delta}=\sqrt{801}=\sqrt{9*89}=\sqrt{9}*\sqrt{89}=3\sqrt{89}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-3\sqrt{89}}{2*2}=\frac{1-3\sqrt{89}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+3\sqrt{89}}{2*2}=\frac{1+3\sqrt{89}}{4}
$