6/x-1/10=9/2x

Solution for 6/x-1/10=9/2x equation:

6/x-1/10=9/2x

We move all terms to the left:

6/x-1/10-(9/2x)=0


Domain of the equation: 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

6/x-(+9/2x)-1/10=0

We get rid of parentheses

6/x-9/2x-1/10=0

We calculate fractions


(-4x^2)/20x^2+120x/20x^2+(-90x)/20x^2=0

We multiply all the terms by the denominator


(-4x^2)+120x+(-90x)=0

We get rid of parentheses

-4x^2+120x-90x=0

We add all the numbers together, and all the variables

-4x^2+30x=0

a = -4; b = 30; c = 0;
Δ = b2-4ac
Δ = 302-4·(-4)·0
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-30}{2*-4}=\frac{-60}{-8}
=7+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+30}{2*-4}=\frac{0}{-8}
=0
$