3/2x+5=8/5x

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

3/2x+5=8/5x

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 5x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


15x/10x^2+(-16x)/10x^2+5=0

We multiply all the terms by the denominator


15x+(-16x)+5*10x^2=0

Wy multiply elements

50x^2+15x+(-16x)=0

We get rid of parentheses

50x^2+15x-16x=0

We add all the numbers together, and all the variables

50x^2-1x=0

a = 50; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·50·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-1}{2*50}=\frac{0}{100}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*50}=\frac{2}{100}
=1/50
$