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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

4x^2-12x-(-2(-2x+6))=0


We calculate terms in parentheses: -(-2(-2x+6)), so:

-2(-2x+6)

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
$