5/3x+6/2x+1=0

Solution for 5/3x+6/2x+1=0 equation:

5/3x+6/2x+1=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We calculate fractions


10x/6x^2+18x/6x^2+1=0

We multiply all the terms by the denominator


10x+18x+1*6x^2=0

We add all the numbers together, and all the variables

28x+1*6x^2=0

Wy multiply elements

6x^2+28x=0

a = 6; b = 28; c = 0;
Δ = b2-4ac
Δ = 282-4·6·0
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-28}{2*6}=\frac{-56}{12}
=-4+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+28}{2*6}=\frac{0}{12}
=0
$