3/2x+2/3x=10

Solution for 3/2x+2/3x=10 equation:

3/2x+2/3x=10

We move all terms to the left:

3/2x+2/3x-(10)=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 calculate fractions


9x/6x^2+4x/6x^2-10=0

We multiply all the terms by the denominator


9x+4x-10*6x^2=0

We add all the numbers together, and all the variables

13x-10*6x^2=0

Wy multiply elements

-60x^2+13x=0

a = -60; b = 13; c = 0;
Δ = b2-4ac
Δ = 132-4·(-60)·0
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-13}{2*-60}=\frac{-26}{-120}
=13/60
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+13}{2*-60}=\frac{0}{-120}
=0
$