19/6x+7=6/2x+9

Solution for 19/6x+7=6/2x+9 equation:

19/6x+7=6/2x+9

We move all terms to the left:

19/6x+7-(6/2x+9)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R



Domain of the equation: 2x+9)!=0

x∈R


We get rid of parentheses

19/6x-6/2x-9+7=0

We calculate fractions


38x/12x^2+(-36x)/12x^2-9+7=0

We add all the numbers together, and all the variables

38x/12x^2+(-36x)/12x^2-2=0

We multiply all the terms by the denominator


38x+(-36x)-2*12x^2=0

Wy multiply elements

-24x^2+38x+(-36x)=0

We get rid of parentheses

-24x^2+38x-36x=0

We add all the numbers together, and all the variables

-24x^2+2x=0

a = -24; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·(-24)·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2}{2*-24}=\frac{-4}{-48}
=1/12
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2}{2*-24}=\frac{0}{-48}
=0
$