(2x-1)*x=127

Solution for (2x-1)*x=127 equation:

(2x-1)*x=127

We move all terms to the left:

(2x-1)*x-(127)=0

We multiply parentheses

2x^2-1x-127=0

a = 2; b = -1; c = -127;
Δ = b2-4ac
Δ = -12-4·2·(-127)
Δ = 1017
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:

$\sqrt{\Delta}=\sqrt{1017}=\sqrt{9*113}=\sqrt{9}*\sqrt{113}=3\sqrt{113}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-3\sqrt{113}}{2*2}=\frac{1-3\sqrt{113}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+3\sqrt{113}}{2*2}=\frac{1+3\sqrt{113}}{4}
$