5/11x+2/3x-1/6=-189

Solution for 5/11x+2/3x-1/6=-189 equation:

5/11x+2/3x-1/6=-189

We move all terms to the left:

5/11x+2/3x-1/6-(-189)=0


Domain of the equation: 11x!=0

x!=0/11

x!=0

x∈R



Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

5/11x+2/3x+189-1/6=0

We calculate fractions


(-99x^2)/1188x^2+540x/1188x^2+792x/1188x^2+189=0

We multiply all the terms by the denominator


(-99x^2)+540x+792x+189*1188x^2=0

We add all the numbers together, and all the variables

(-99x^2)+1332x+189*1188x^2=0

Wy multiply elements

(-99x^2)+224532x^2+1332x=0

We get rid of parentheses

-99x^2+224532x^2+1332x=0

We add all the numbers together, and all the variables

224433x^2+1332x=0

a = 224433; b = 1332; c = 0;
Δ = b2-4ac
Δ = 13322-4·224433·0
Δ = 1774224
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1774224}=1332$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1332)-1332}{2*224433}=\frac{-2664}{448866}
=-148/24937
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1332)+1332}{2*224433}=\frac{0}{448866}
=0
$