x/3x+5x+10=4x+8

Solution for x/3x+5x+10=4x+8 equation:

x/3x+5x+10=4x+8

We move all terms to the left:

x/3x+5x+10-(4x+8)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

5x+x/3x-(4x+8)+10=0

We get rid of parentheses

5x+x/3x-4x-8+10=0

We multiply all the terms by the denominator


5x*3x+x-4x*3x-8*3x+10*3x=0

We add all the numbers together, and all the variables

x+5x*3x-4x*3x-8*3x+10*3x=0

Wy multiply elements

15x^2-12x^2+x-24x+30x=0

We add all the numbers together, and all the variables

3x^2+7x=0

a = 3; b = 7; c = 0;
Δ = b2-4ac
Δ = 72-4·3·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-7}{2*3}=\frac{-14}{6}
=-2+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7}{2*3}=\frac{0}{6}
=0
$