2x(x-3)=4x-6

Solution for 2x(x-3)=4x-6 equation:

2x(x-3)=4x-6

We move all terms to the left:

2x(x-3)-(4x-6)=0

We multiply parentheses

2x^2-6x-(4x-6)=0

We get rid of parentheses

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

We add all the numbers together, and all the variables

2x^2-10x+6=0

a = 2; b = -10; c = +6;
Δ = b2-4ac
Δ = -102-4·2·6
Δ = 52
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:

$\sqrt{\Delta}=\sqrt{52}=\sqrt{4*13}=\sqrt{4}*\sqrt{13}=2\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{13}}{2*2}=\frac{10-2\sqrt{13}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{13}}{2*2}=\frac{10+2\sqrt{13}}{4}
$