3+12/5x=2+1/4x-1

Solution for 3+12/5x=2+1/4x-1 equation:

3+12/5x=2+1/4x-1

We move all terms to the left:

3+12/5x-(2+1/4x-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 add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


48x/20x^2+(-5x)/20x^2-1+3=0

We add all the numbers together, and all the variables

48x/20x^2+(-5x)/20x^2+2=0

We multiply all the terms by the denominator


48x+(-5x)+2*20x^2=0

Wy multiply elements

40x^2+48x+(-5x)=0

We get rid of parentheses

40x^2+48x-5x=0

We add all the numbers together, and all the variables

40x^2+43x=0

a = 40; b = 43; c = 0;
Δ = b2-4ac
Δ = 432-4·40·0
Δ = 1849
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1849}=43$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(43)-43}{2*40}=\frac{-86}{80}
=-1+3/40
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(43)+43}{2*40}=\frac{0}{80}
=0
$