7/x=1/2x+52

Solution for 7/x=1/2x+52 equation:

7/x=1/2x+52

We move all terms to the left:

7/x-(1/2x+52)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 2x+52)!=0

x∈R


We get rid of parentheses

7/x-1/2x-52=0

We calculate fractions


14x/2x^2+(-x)/2x^2-52=0

We add all the numbers together, and all the variables

14x/2x^2+(-1x)/2x^2-52=0

We multiply all the terms by the denominator


14x+(-1x)-52*2x^2=0

Wy multiply elements

-104x^2+14x+(-1x)=0

We get rid of parentheses

-104x^2+14x-1x=0

We add all the numbers together, and all the variables

-104x^2+13x=0

a = -104; b = 13; c = 0;
Δ = b2-4ac
Δ = 132-4·(-104)·0
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-13}{2*-104}=\frac{-26}{-208}
=1/8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+13}{2*-104}=\frac{0}{-208}
=0
$