7/2x+141/2=7/x-10

Solution for 7/2x+141/2=7/x-10 equation:

7/2x+141/2=7/x-10

We move all terms to the left:

7/2x+141/2-(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+141/2=0

We calculate fractions


7x/8x^2+(-56x)/8x^2+141x/8x^2+10=0

We multiply all the terms by the denominator


7x+(-56x)+141x+10*8x^2=0

We add all the numbers together, and all the variables

148x+(-56x)+10*8x^2=0

Wy multiply elements

80x^2+148x+(-56x)=0

We get rid of parentheses

80x^2+148x-56x=0

We add all the numbers together, and all the variables

80x^2+92x=0

a = 80; b = 92; c = 0;
Δ = b2-4ac
Δ = 922-4·80·0
Δ = 8464
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{8464}=92$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(92)-92}{2*80}=\frac{-184}{160}
=-1+3/20
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(92)+92}{2*80}=\frac{0}{160}
=0
$