-2x(x-1)=53x

Solution for -2x(x-1)=53x equation:

-2x(x-1)=53x

We move all terms to the left:

-2x(x-1)-(53x)=0

We add all the numbers together, and all the variables

-53x-2x(x-1)=0

We multiply parentheses

-2x^2-53x+2x=0

We add all the numbers together, and all the variables

-2x^2-51x=0

a = -2; b = -51; c = 0;
Δ = b2-4ac
Δ = -512-4·(-2)·0
Δ = 2601
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2601}=51$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-51)-51}{2*-2}=\frac{0}{-4}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-51)+51}{2*-2}=\frac{102}{-4}
=-25+1/2
$