5/x+5/2x=65

Solution for 5/x+5/2x=65 equation:

5/x+5/2x=65

We move all terms to the left:

5/x+5/2x-(65)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We calculate fractions


10x/2x^2+5x/2x^2-65=0

We multiply all the terms by the denominator


10x+5x-65*2x^2=0

We add all the numbers together, and all the variables

15x-65*2x^2=0

Wy multiply elements

-130x^2+15x=0

a = -130; b = 15; c = 0;
Δ = b2-4ac
Δ = 152-4·(-130)·0
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-15}{2*-130}=\frac{-30}{-260}
=3/26
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+15}{2*-130}=\frac{0}{-260}
=0
$