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

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

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

We move all terms to the left:

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

We multiply parentheses

4x-(3x(x-2))+8=0


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

3x(x-2)

We multiply parentheses

3x^2-6x

Back to the equation:

-(3x^2-6x)


We get rid of parentheses

-3x^2+4x+6x+8=0

We add all the numbers together, and all the variables

-3x^2+10x+8=0

a = -3; b = 10; c = +8;
Δ = b2-4ac
Δ = 102-4·(-3)·8
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-14}{2*-3}=\frac{-24}{-6}
=+4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+14}{2*-3}=\frac{4}{-6}
=-2/3
$