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

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

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

We move all terms to the left:

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

We multiply parentheses

4x^2-12x-(4(x-3))=0


We calculate terms in parentheses: -(4(x-3)), so:

4(x-3)

We multiply parentheses

4x-12

Back to the equation:

-(4x-12)


We get rid of parentheses

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

We add all the numbers together, and all the variables

4x^2-16x+12=0

a = 4; b = -16; c = +12;
Δ = b2-4ac
Δ = -162-4·4·12
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-8}{2*4}=\frac{8}{8}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+8}{2*4}=\frac{24}{8}
=3
$