3+12/5x=21/4x-1

Solution for 3+12/5x=21/4x-1 equation:

3+12/5x=21/4x-1

We move all terms to the left:

3+12/5x-(21/4x-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-21/4x+1+3=0

We calculate fractions


48x/20x^2+(-105x)/20x^2+1+3=0

We add all the numbers together, and all the variables

48x/20x^2+(-105x)/20x^2+4=0

We multiply all the terms by the denominator


48x+(-105x)+4*20x^2=0

Wy multiply elements

80x^2+48x+(-105x)=0

We get rid of parentheses

80x^2+48x-105x=0

We add all the numbers together, and all the variables

80x^2-57x=0

a = 80; b = -57; c = 0;
Δ = b2-4ac
Δ = -572-4·80·0
Δ = 3249
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3249}=57$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-57)-57}{2*80}=\frac{0}{160}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-57)+57}{2*80}=\frac{114}{160}
=57/80
$