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

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

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

We move all terms to the left:

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


We calculate terms in parentheses: -(x(2x-3)), so:

x(2x-3)

We multiply parentheses

2x^2-3x

Back to the equation:

-(2x^2-3x)


We get rid of parentheses

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

We add all the numbers together, and all the variables

-2x^2+7x-1=0

a = -2; b = 7; c = -1;
Δ = b2-4ac
Δ = 72-4·(-2)·(-1)
Δ = 41
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{-(7)-\sqrt{41}}{2*-2}=\frac{-7-\sqrt{41}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{41}}{2*-2}=\frac{-7+\sqrt{41}}{-4}
$