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

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

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

We move all terms to the left:

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

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

We get rid of parentheses

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

We calculate fractions


40x/24x^2+3x/24x^2+(-9x)/24x^2-5=0

We multiply all the terms by the denominator


40x+3x+(-9x)-5*24x^2=0

We add all the numbers together, and all the variables

43x+(-9x)-5*24x^2=0

Wy multiply elements

-120x^2+43x+(-9x)=0

We get rid of parentheses

-120x^2+43x-9x=0

We add all the numbers together, and all the variables

-120x^2+34x=0

a = -120; b = 34; c = 0;
Δ = b2-4ac
Δ = 342-4·(-120)·0
Δ = 1156
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1156}=34$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(34)-34}{2*-120}=\frac{-68}{-240}
=17/60
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(34)+34}{2*-120}=\frac{0}{-240}
=0
$