21/9x+1=24/11x-1

Solution for 21/9x+1=24/11x-1 equation:

21/9x+1=24/11x-1

We move all terms to the left:

21/9x+1-(24/11x-1)=0


Domain of the equation: 9x!=0

x!=0/9

x!=0

x∈R



Domain of the equation: 11x-1)!=0

x∈R


We get rid of parentheses

21/9x-24/11x+1+1=0

We calculate fractions


231x/99x^2+(-216x)/99x^2+1+1=0

We add all the numbers together, and all the variables

231x/99x^2+(-216x)/99x^2+2=0

We multiply all the terms by the denominator


231x+(-216x)+2*99x^2=0

Wy multiply elements

198x^2+231x+(-216x)=0

We get rid of parentheses

198x^2+231x-216x=0

We add all the numbers together, and all the variables

198x^2+15x=0

a = 198; b = 15; c = 0;
Δ = b2-4ac
Δ = 152-4·198·0
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-15}{2*198}=\frac{-30}{396}
=-5/66
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+15}{2*198}=\frac{0}{396}
=0
$