5/2x-2/3x=-3/8

Solution for 5/2x-2/3x=-3/8 equation:

5/2x-2/3x=-3/8

We move all terms to the left:

5/2x-2/3x-(-3/8)=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 get rid of parentheses

5/2x-2/3x+3/8=0

We calculate fractions


54x^2/384x^2+960x/384x^2+(-256x)/384x^2=0

We multiply all the terms by the denominator


54x^2+960x+(-256x)=0

We get rid of parentheses

54x^2+960x-256x=0

We add all the numbers together, and all the variables

54x^2+704x=0

a = 54; b = 704; c = 0;
Δ = b2-4ac
Δ = 7042-4·54·0
Δ = 495616
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{495616}=704$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(704)-704}{2*54}=\frac{-1408}{108}
=-13+1/27
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(704)+704}{2*54}=\frac{0}{108}
=0
$