1/3x+9=3/4x+-1

Solution for 1/3x+9=3/4x+-1 equation:

1/3x+9=3/4x+-1

We move all terms to the left:

1/3x+9-(3/4x+-1)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 4x+-1)!=0

x∈R


We add all the numbers together, and all the variables

1/3x-(3/4x-1)+9=0

We get rid of parentheses

1/3x-3/4x+1+9=0

We calculate fractions


4x/12x^2+(-9x)/12x^2+1+9=0

We add all the numbers together, and all the variables

4x/12x^2+(-9x)/12x^2+10=0

We multiply all the terms by the denominator


4x+(-9x)+10*12x^2=0

Wy multiply elements

120x^2+4x+(-9x)=0

We get rid of parentheses

120x^2+4x-9x=0

We add all the numbers together, and all the variables

120x^2-5x=0

a = 120; b = -5; c = 0;
Δ = b2-4ac
Δ = -52-4·120·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5}{2*120}=\frac{0}{240}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5}{2*120}=\frac{10}{240}
=1/24
$