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

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

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

We move all terms to the left:

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


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

3x(x-2)

We multiply parentheses

3x^2-6x

Back to the equation:

-(3x^2-6x)


We get rid of parentheses

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

We add all the numbers together, and all the variables

-3x^2+10x-1=0

a = -3; b = 10; c = -1;
Δ = b2-4ac
Δ = 102-4·(-3)·(-1)
Δ = 88
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:

$\sqrt{\Delta}=\sqrt{88}=\sqrt{4*22}=\sqrt{4}*\sqrt{22}=2\sqrt{22}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{22}}{2*-3}=\frac{-10-2\sqrt{22}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{22}}{2*-3}=\frac{-10+2\sqrt{22}}{-6}
$