3x-4(x-3)=x(x-4)

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

3x-4(x-3)=x(x-4)

We move all terms to the left:

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

We multiply parentheses

3x-4x-(x(x-4))+12=0


We calculate terms in parentheses: -(x(x-4)), so:

x(x-4)

We multiply parentheses

x^2-4x

Back to the equation:

-(x^2-4x)


We add all the numbers together, and all the variables

-1x-(x^2-4x)+12=0

We get rid of parentheses

-x^2-1x+4x+12=0

We add all the numbers together, and all the variables

-1x^2+3x+12=0

a = -1; b = 3; c = +12;
Δ = b2-4ac
Δ = 32-4·(-1)·12
Δ = 57
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{-(3)-\sqrt{57}}{2*-1}=\frac{-3-\sqrt{57}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{57}}{2*-1}=\frac{-3+\sqrt{57}}{-2}
$