5/x=29/10x+3

Solution for 5/x=29/10x+3 equation:

5/x=29/10x+3

We move all terms to the left:

5/x-(29/10x+3)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 10x+3)!=0

x∈R


We get rid of parentheses

5/x-29/10x-3=0

We calculate fractions


50x/10x^2+(-29x)/10x^2-3=0

We multiply all the terms by the denominator


50x+(-29x)-3*10x^2=0

Wy multiply elements

-30x^2+50x+(-29x)=0

We get rid of parentheses

-30x^2+50x-29x=0

We add all the numbers together, and all the variables

-30x^2+21x=0

a = -30; b = 21; c = 0;
Δ = b2-4ac
Δ = 212-4·(-30)·0
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-21}{2*-30}=\frac{-42}{-60}
=7/10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+21}{2*-30}=\frac{0}{-60}
=0
$