52/x+3=91/2x-1

Solution for 52/x+3=91/2x-1 equation:

52/x+3=91/2x-1

We move all terms to the left:

52/x+3-(91/2x-1)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 2x-1)!=0

x∈R


We get rid of parentheses

52/x-91/2x+1+3=0

We calculate fractions


104x/2x^2+(-91x)/2x^2+1+3=0

We add all the numbers together, and all the variables

104x/2x^2+(-91x)/2x^2+4=0

We multiply all the terms by the denominator


104x+(-91x)+4*2x^2=0

Wy multiply elements

8x^2+104x+(-91x)=0

We get rid of parentheses

8x^2+104x-91x=0

We add all the numbers together, and all the variables

8x^2+13x=0

a = 8; b = 13; c = 0;
Δ = b2-4ac
Δ = 132-4·8·0
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*8}=\frac{-26}{16}
=-1+5/8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+13}{2*8}=\frac{0}{16}
=0
$