3x+4x+5x=4x(x+2)

Solution for 3x+4x+5x=4x(x+2) equation:

3x+4x+5x=4x(x+2)

We move all terms to the left:

3x+4x+5x-(4x(x+2))=0

We add all the numbers together, and all the variables

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


We calculate terms in parentheses: -(4x(x+2)), so:

4x(x+2)

We multiply parentheses

4x^2+8x

Back to the equation:

-(4x^2+8x)


We get rid of parentheses

-4x^2+12x-8x=0

We add all the numbers together, and all the variables

-4x^2+4x=0

a = -4; b = 4; c = 0;
Δ = b2-4ac
Δ = 42-4·(-4)·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4}{2*-4}=\frac{-8}{-8}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4}{2*-4}=\frac{0}{-8}
=0
$