3/2x+1/3x=5+1/2

Solution for 3/2x+1/3x=5+1/2 equation:

3/2x+1/3x=5+1/2

We move all terms to the left:

3/2x+1/3x-(5+1/2)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

3/2x+1/3x-(1/2+5)=0

We get rid of parentheses

3/2x+1/3x-5-1/2=0

We calculate fractions


9x/24x^2+8x/24x^2+(-3x)/24x^2-5=0

We multiply all the terms by the denominator


9x+8x+(-3x)-5*24x^2=0

We add all the numbers together, and all the variables

17x+(-3x)-5*24x^2=0

Wy multiply elements

-120x^2+17x+(-3x)=0

We get rid of parentheses

-120x^2+17x-3x=0

We add all the numbers together, and all the variables

-120x^2+14x=0

a = -120; b = 14; c = 0;
Δ = b2-4ac
Δ = 142-4·(-120)·0
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-14}{2*-120}=\frac{-28}{-240}
=7/60
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+14}{2*-120}=\frac{0}{-240}
=0
$