x/3x+9-2x+5=6x-4x+7

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Solution for x/3x+9-2x+5=6x-4x+7 equation:



x/3x+9-2x+5=6x-4x+7
We move all terms to the left:
x/3x+9-2x+5-(6x-4x+7)=0
Domain of the equation: 3x!=0
x!=0/3
x!=0
x∈R
We add all the numbers together, and all the variables
x/3x-2x-(2x+7)+9+5=0
We add all the numbers together, and all the variables
-2x+x/3x-(2x+7)+14=0
We get rid of parentheses
-2x+x/3x-2x-7+14=0
We multiply all the terms by the denominator
-2x*3x+x-2x*3x-7*3x+14*3x=0
We add all the numbers together, and all the variables
x-2x*3x-2x*3x-7*3x+14*3x=0
Wy multiply elements
-6x^2-6x^2+x-21x+42x=0
We add all the numbers together, and all the variables
-12x^2+22x=0
a = -12; b = 22; c = 0;
Δ = b2-4ac
Δ = 222-4·(-12)·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*-12}=\frac{-44}{-24} =1+5/6 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+22}{2*-12}=\frac{0}{-24} =0 $

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