2/3x=-3/2x+13

Solution for 2/3x=-3/2x+13 equation:

2/3x=-3/2x+13

We move all terms to the left:

2/3x-(-3/2x+13)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 2x+13)!=0

x∈R


We get rid of parentheses

2/3x+3/2x-13=0

We calculate fractions


4x/6x^2+9x/6x^2-13=0

We multiply all the terms by the denominator


4x+9x-13*6x^2=0

We add all the numbers together, and all the variables

13x-13*6x^2=0

Wy multiply elements

-78x^2+13x=0

a = -78; b = 13; c = 0;
Δ = b2-4ac
Δ = 132-4·(-78)·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*-78}=\frac{-26}{-156}
=1/6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+13}{2*-78}=\frac{0}{-156}
=0
$