(2x-1)*(-3x+4)=x

Solution for (2x-1)*(-3x+4)=x equation:

(2x-1)(-3x+4)=x

We move all terms to the left:

(2x-1)(-3x+4)-(x)=0

We add all the numbers together, and all the variables

-1x+(2x-1)(-3x+4)=0

We multiply parentheses ..

(-6x^2+8x+3x-4)-1x=0

We get rid of parentheses

-6x^2+8x+3x-1x-4=0

We add all the numbers together, and all the variables

-6x^2+10x-4=0

a = -6; b = 10; c = -4;
Δ = b2-4ac
Δ = 102-4·(-6)·(-4)
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2}{2*-6}=\frac{-12}{-12}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2}{2*-6}=\frac{-8}{-12}
=2/3
$