7/2x+29/2=7/x-10

Solution for 7/2x+29/2=7/x-10 equation:

7/2x+29/2=7/x-10

We move all terms to the left:

7/2x+29/2-(7/x-10)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: x-10)!=0

x∈R


We get rid of parentheses

7/2x-7/x+10+29/2=0

We calculate fractions


7x/8x^2+(-56x)/8x^2+29x/8x^2+10=0

We multiply all the terms by the denominator


7x+(-56x)+29x+10*8x^2=0

We add all the numbers together, and all the variables

36x+(-56x)+10*8x^2=0

Wy multiply elements

80x^2+36x+(-56x)=0

We get rid of parentheses

80x^2+36x-56x=0

We add all the numbers together, and all the variables

80x^2-20x=0

a = 80; b = -20; c = 0;
Δ = b2-4ac
Δ = -202-4·80·0
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-20}{2*80}=\frac{0}{160}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+20}{2*80}=\frac{40}{160}
=1/4
$