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

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

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

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 6x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


42x/12x^2+(-4x)/12x^2-7+9=0

We add all the numbers together, and all the variables

42x/12x^2+(-4x)/12x^2+2=0

We multiply all the terms by the denominator


42x+(-4x)+2*12x^2=0

Wy multiply elements

24x^2+42x+(-4x)=0

We get rid of parentheses

24x^2+42x-4x=0

We add all the numbers together, and all the variables

24x^2+38x=0

a = 24; b = 38; c = 0;
Δ = b2-4ac
Δ = 382-4·24·0
Δ = 1444
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1444}=38$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(38)-38}{2*24}=\frac{-76}{48}
=-1+7/12
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(38)+38}{2*24}=\frac{0}{48}
=0
$