10/x=3/2x+1

Solution for 10/x=3/2x+1 equation:

10/x=3/2x+1

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



Domain of the equation: 2x+1)!=0

x∈R


We get rid of parentheses

10/x-3/2x-1=0

We calculate fractions


20x/2x^2+(-3x)/2x^2-1=0

We multiply all the terms by the denominator


20x+(-3x)-1*2x^2=0

Wy multiply elements

-2x^2+20x+(-3x)=0

We get rid of parentheses

-2x^2+20x-3x=0

We add all the numbers together, and all the variables

-2x^2+17x=0

a = -2; b = 17; c = 0;
Δ = b2-4ac
Δ = 172-4·(-2)·0
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-17}{2*-2}=\frac{-34}{-4}
=8+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+17}{2*-2}=\frac{0}{-4}
=0
$