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

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

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

We move all terms to the left:

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

We multiply parentheses

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


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

2x(x-3)

We multiply parentheses

2x^2-6x

Back to the equation:

-(2x^2-6x)


We get rid of parentheses

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

We add all the numbers together, and all the variables

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

a = -2; b = 10; c = -4;
Δ = b2-4ac
Δ = 102-4·(-2)·(-4)
Δ = 68
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:

$\sqrt{\Delta}=\sqrt{68}=\sqrt{4*17}=\sqrt{4}*\sqrt{17}=2\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{17}}{2*-2}=\frac{-10-2\sqrt{17}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{17}}{2*-2}=\frac{-10+2\sqrt{17}}{-4}
$