5/x+1/2x=17/14

Solution for 5/x+1/2x=17/14 equation:

5/x+1/2x=17/14

We move all terms to the left:

5/x+1/2x-(17/14)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

5/x+1/2x-(+17/14)=0

We get rid of parentheses

5/x+1/2x-17/14=0

We calculate fractions


(-68x^2)/28x^2+140x/28x^2+14x/28x^2=0

We multiply all the terms by the denominator


(-68x^2)+140x+14x=0

We add all the numbers together, and all the variables

(-68x^2)+154x=0

We get rid of parentheses

-68x^2+154x=0

a = -68; b = 154; c = 0;
Δ = b2-4ac
Δ = 1542-4·(-68)·0
Δ = 23716
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{23716}=154$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(154)-154}{2*-68}=\frac{-308}{-136}
=2+9/34
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(154)+154}{2*-68}=\frac{0}{-136}
=0
$