7/3x+-3/2+5/2x=31/18

Solution for 7/3x+-3/2+5/2x=31/18 equation:

7/3x+-3/2+5/2x=31/18

We move all terms to the left:

7/3x+-3/2+5/2x-(31/18)=0


Domain of the equation: 3x!=0

x!=0/3

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

7/3x+5/2x+-3/2-(+31/18)=0

We add all the numbers together, and all the variables

7/3x+5/2x-3/2-(+31/18)=0

We get rid of parentheses

7/3x+5/2x-3/2-31/18=0

We calculate fractions


(-744x^2)/432x^2+1008x/432x^2+270x/432x^2+(-162x)/432x^2=0

We multiply all the terms by the denominator


(-744x^2)+1008x+270x+(-162x)=0

We add all the numbers together, and all the variables

(-744x^2)+1278x+(-162x)=0

We get rid of parentheses

-744x^2+1278x-162x=0

We add all the numbers together, and all the variables

-744x^2+1116x=0

a = -744; b = 1116; c = 0;
Δ = b2-4ac
Δ = 11162-4·(-744)·0
Δ = 1245456
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1245456}=1116$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1116)-1116}{2*-744}=\frac{-2232}{-1488}
=1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1116)+1116}{2*-744}=\frac{0}{-1488}
=0
$