11/2x+16=4-2/3x

Solution for 11/2x+16=4-2/3x equation:

11/2x+16=4-2/3x

We move all terms to the left:

11/2x+16-(4-2/3x)=0


Domain of the equation: 2x!=0

x!=0/2

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

11/2x-(-2/3x+4)+16=0

We get rid of parentheses

11/2x+2/3x-4+16=0

We calculate fractions


33x/6x^2+4x/6x^2-4+16=0

We add all the numbers together, and all the variables

33x/6x^2+4x/6x^2+12=0

We multiply all the terms by the denominator


33x+4x+12*6x^2=0

We add all the numbers together, and all the variables

37x+12*6x^2=0

Wy multiply elements

72x^2+37x=0

a = 72; b = 37; c = 0;
Δ = b2-4ac
Δ = 372-4·72·0
Δ = 1369
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1369}=37$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(37)-37}{2*72}=\frac{-74}{144}
=-37/72
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(37)+37}{2*72}=\frac{0}{144}
=0
$