3+12/5x=9/4x-1

Solution for 3+12/5x=9/4x-1 equation:

3+12/5x=9/4x-1

We move all terms to the left:

3+12/5x-(9/4x-1)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 4x-1)!=0

x∈R


We get rid of parentheses

12/5x-9/4x+1+3=0

We calculate fractions


48x/20x^2+(-45x)/20x^2+1+3=0

We add all the numbers together, and all the variables

48x/20x^2+(-45x)/20x^2+4=0

We multiply all the terms by the denominator


48x+(-45x)+4*20x^2=0

Wy multiply elements

80x^2+48x+(-45x)=0

We get rid of parentheses

80x^2+48x-45x=0

We add all the numbers together, and all the variables

80x^2+3x=0

a = 80; b = 3; c = 0;
Δ = b2-4ac
Δ = 32-4·80·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3}{2*80}=\frac{-6}{160}
=-3/80
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3}{2*80}=\frac{0}{160}
=0
$