7/x-18/5x=-1/2

Solution for 7/x-18/5x=-1/2 equation:

7/x-18/5x=-1/2

We move all terms to the left:

7/x-18/5x-(-1/2)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

7/x-18/5x+1/2=0

We calculate fractions


25x^2/20x^2+140x/20x^2+(-72x)/20x^2=0

We multiply all the terms by the denominator


25x^2+140x+(-72x)=0

We get rid of parentheses

25x^2+140x-72x=0

We add all the numbers together, and all the variables

25x^2+68x=0

a = 25; b = 68; c = 0;
Δ = b2-4ac
Δ = 682-4·25·0
Δ = 4624
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4624}=68$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(68)-68}{2*25}=\frac{-136}{50}
=-2+18/25
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(68)+68}{2*25}=\frac{0}{50}
=0
$