8/x=3/2x+65

Solution for 8/x=3/2x+65 equation:

8/x=3/2x+65

We move all terms to the left:

8/x-(3/2x+65)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 2x+65)!=0

x∈R


We get rid of parentheses

8/x-3/2x-65=0

We calculate fractions


16x/2x^2+(-3x)/2x^2-65=0

We multiply all the terms by the denominator


16x+(-3x)-65*2x^2=0

Wy multiply elements

-130x^2+16x+(-3x)=0

We get rid of parentheses

-130x^2+16x-3x=0

We add all the numbers together, and all the variables

-130x^2+13x=0

a = -130; b = 13; c = 0;
Δ = b2-4ac
Δ = 132-4·(-130)·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*-130}=\frac{-26}{-260}
=1/10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+13}{2*-130}=\frac{0}{-260}
=0
$