2/x-3/5x-1/10=0

Solution for 2/x-3/5x-1/10=0 equation:

2/x-3/5x-1/10=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We calculate fractions


(-25x^2)/50x^2+100x/50x^2+(-30x)/50x^2=0

We multiply all the terms by the denominator


(-25x^2)+100x+(-30x)=0

We get rid of parentheses

-25x^2+100x-30x=0

We add all the numbers together, and all the variables

-25x^2+70x=0

a = -25; b = 70; c = 0;
Δ = b2-4ac
Δ = 702-4·(-25)·0
Δ = 4900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4900}=70$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(70)-70}{2*-25}=\frac{-140}{-50}
=2+4/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(70)+70}{2*-25}=\frac{0}{-50}
=0
$