4/2x+5/3X=16

Solution for 4/2x+5/3X=16 equation:

4/2x+5/3x=16

We move all terms to the left:

4/2x+5/3x-(16)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We calculate fractions


12x/6x^2+10x/6x^2-16=0

We multiply all the terms by the denominator


12x+10x-16*6x^2=0

We add all the numbers together, and all the variables

22x-16*6x^2=0

Wy multiply elements

-96x^2+22x=0

a = -96; b = 22; c = 0;
Δ = b2-4ac
Δ = 222-4·(-96)·0
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-22}{2*-96}=\frac{-44}{-192}
=11/48
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+22}{2*-96}=\frac{0}{-192}
=0
$