12/5x-31/4=3/2x

Solution for 12/5x-31/4=3/2x equation:

12/5x-31/4=3/2x

We move all terms to the left:

12/5x-31/4-(3/2x)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

12/5x-(+3/2x)-31/4=0

We get rid of parentheses

12/5x-3/2x-31/4=0

We calculate fractions


(-620x^2)/160x^2+384x/160x^2+(-240x)/160x^2=0

We multiply all the terms by the denominator


(-620x^2)+384x+(-240x)=0

We get rid of parentheses

-620x^2+384x-240x=0

We add all the numbers together, and all the variables

-620x^2+144x=0

a = -620; b = 144; c = 0;
Δ = b2-4ac
Δ = 1442-4·(-620)·0
Δ = 20736
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{20736}=144$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(144)-144}{2*-620}=\frac{-288}{-1240}
=36/155
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(144)+144}{2*-620}=\frac{0}{-1240}
=0
$