3+2/5x=112/3x

Solution for 3+2/5x=112/3x equation:

3+2/5x=112/3x

We move all terms to the left:

3+2/5x-(112/3x)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

2/5x-(+112/3x)+3=0

We get rid of parentheses

2/5x-112/3x+3=0

We calculate fractions


6x/15x^2+(-560x)/15x^2+3=0

We multiply all the terms by the denominator


6x+(-560x)+3*15x^2=0

Wy multiply elements

45x^2+6x+(-560x)=0

We get rid of parentheses

45x^2+6x-560x=0

We add all the numbers together, and all the variables

45x^2-554x=0

a = 45; b = -554; c = 0;
Δ = b2-4ac
Δ = -5542-4·45·0
Δ = 306916
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{306916}=554$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-554)-554}{2*45}=\frac{0}{90}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-554)+554}{2*45}=\frac{1108}{90}
=12+14/45
$