5/2x-1/3x=17/18

Solution for 5/2x-1/3x=17/18 equation:

5/2x-1/3x=17/18

We move all terms to the left:

5/2x-1/3x-(17/18)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

5/2x-1/3x-(+17/18)=0

We get rid of parentheses

5/2x-1/3x-17/18=0

We calculate fractions


(-306x^2)/108x^2+270x/108x^2+(-36x)/108x^2=0

We multiply all the terms by the denominator


(-306x^2)+270x+(-36x)=0

We get rid of parentheses

-306x^2+270x-36x=0

We add all the numbers together, and all the variables

-306x^2+234x=0

a = -306; b = 234; c = 0;
Δ = b2-4ac
Δ = 2342-4·(-306)·0
Δ = 54756
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{54756}=234$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(234)-234}{2*-306}=\frac{-468}{-612}
=13/17
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(234)+234}{2*-306}=\frac{0}{-612}
=0
$