33/5x+2=1/2x=3

Solution for 33/5x+2=1/2x=3 equation:

33/5x+2=1/2x=3

We move all terms to the left:

33/5x+2-(1/2x)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

33/5x-(+1/2x)+2=0

We get rid of parentheses

33/5x-1/2x+2=0

We calculate fractions


66x/10x^2+(-5x)/10x^2+2=0

We multiply all the terms by the denominator


66x+(-5x)+2*10x^2=0

Wy multiply elements

20x^2+66x+(-5x)=0

We get rid of parentheses

20x^2+66x-5x=0

We add all the numbers together, and all the variables

20x^2+61x=0

a = 20; b = 61; c = 0;
Δ = b2-4ac
Δ = 612-4·20·0
Δ = 3721
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3721}=61$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(61)-61}{2*20}=\frac{-122}{40}
=-3+1/20
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(61)+61}{2*20}=\frac{0}{40}
=0
$