x/3x-2x=4x+15

Solution for x/3x-2x=4x+15 equation:

x/3x-2x=4x+15

We move all terms to the left:

x/3x-2x-(4x+15)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

-2x+x/3x-(4x+15)=0

We get rid of parentheses

-2x+x/3x-4x-15=0

We multiply all the terms by the denominator


-2x*3x+x-4x*3x-15*3x=0

We add all the numbers together, and all the variables

x-2x*3x-4x*3x-15*3x=0

Wy multiply elements

-6x^2-12x^2+x-45x=0

We add all the numbers together, and all the variables

-18x^2-44x=0

a = -18; b = -44; c = 0;
Δ = b2-4ac
Δ = -442-4·(-18)·0
Δ = 1936
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1936}=44$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-44)-44}{2*-18}=\frac{0}{-36}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-44)+44}{2*-18}=\frac{88}{-36}
=-2+4/9
$