3+12/5x=9/2x-1

Solution for 3+12/5x=9/2x-1 equation:

3+12/5x=9/2x-1

We move all terms to the left:

3+12/5x-(9/2x-1)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 2x-1)!=0

x∈R


We get rid of parentheses

12/5x-9/2x+1+3=0

We calculate fractions


24x/10x^2+(-45x)/10x^2+1+3=0

We add all the numbers together, and all the variables

24x/10x^2+(-45x)/10x^2+4=0

We multiply all the terms by the denominator


24x+(-45x)+4*10x^2=0

Wy multiply elements

40x^2+24x+(-45x)=0

We get rid of parentheses

40x^2+24x-45x=0

We add all the numbers together, and all the variables

40x^2-21x=0

a = 40; b = -21; c = 0;
Δ = b2-4ac
Δ = -212-4·40·0
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-21}{2*40}=\frac{0}{80}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+21}{2*40}=\frac{42}{80}
=21/40
$