8/3x+2=7/2x

Solution for 8/3x+2=7/2x equation:

8/3x+2=7/2x

We move all terms to the left:

8/3x+2-(7/2x)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

8/3x-(+7/2x)+2=0

We get rid of parentheses

8/3x-7/2x+2=0

We calculate fractions


16x/6x^2+(-21x)/6x^2+2=0

We multiply all the terms by the denominator


16x+(-21x)+2*6x^2=0

Wy multiply elements

12x^2+16x+(-21x)=0

We get rid of parentheses

12x^2+16x-21x=0

We add all the numbers together, and all the variables

12x^2-5x=0

a = 12; b = -5; c = 0;
Δ = b2-4ac
Δ = -52-4·12·0
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*12}=\frac{0}{24}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5}{2*12}=\frac{10}{24}
=5/12
$