4(x-2)+3x=7x-3x(x-2)

Solution for 4(x-2)+3x=7x-3x(x-2) equation:

4(x-2)+3x=7x-3x(x-2)

We move all terms to the left:

4(x-2)+3x-(7x-3x(x-2))=0

We add all the numbers together, and all the variables

3x+4(x-2)-(7x-3x(x-2))=0

We multiply parentheses

3x+4x-(7x-3x(x-2))-8=0


We calculate terms in parentheses: -(7x-3x(x-2)), so:

7x-3x(x-2)

We multiply parentheses

-3x^2+7x+6x

We add all the numbers together, and all the variables

-3x^2+13x

Back to the equation:

-(-3x^2+13x)


We add all the numbers together, and all the variables

-(-3x^2+13x)+7x-8=0

We get rid of parentheses

3x^2-13x+7x-8=0

We add all the numbers together, and all the variables

3x^2-6x-8=0

a = 3; b = -6; c = -8;
Δ = b2-4ac
Δ = -62-4·3·(-8)
Δ = 132
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:

$\sqrt{\Delta}=\sqrt{132}=\sqrt{4*33}=\sqrt{4}*\sqrt{33}=2\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{33}}{2*3}=\frac{6-2\sqrt{33}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{33}}{2*3}=\frac{6+2\sqrt{33}}{6}
$