1/2x=10-1/3x

Solution for 1/2x=10-1/3x equation:

1/2x=10-1/3x

We move all terms to the left:

1/2x-(10-1/3x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

1/2x-(-1/3x+10)=0

We get rid of parentheses

1/2x+1/3x-10=0

We calculate fractions


3x/6x^2+2x/6x^2-10=0

We multiply all the terms by the denominator


3x+2x-10*6x^2=0

We add all the numbers together, and all the variables

5x-10*6x^2=0

Wy multiply elements

-60x^2+5x=0

a = -60; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·(-60)·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5}{2*-60}=\frac{-10}{-120}
=1/12
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*-60}=\frac{0}{-120}
=0
$