5/12x+2/3x-1/6=-189

Solution for 5/12x+2/3x-1/6=-189 equation:

5/12x+2/3x-1/6=-189

We move all terms to the left:

5/12x+2/3x-1/6-(-189)=0


Domain of the equation: 12x!=0

x!=0/12

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

5/12x+2/3x+189-1/6=0

We calculate fractions


(-108x^2)/1296x^2+540x/1296x^2+864x/1296x^2+189=0

We multiply all the terms by the denominator


(-108x^2)+540x+864x+189*1296x^2=0

We add all the numbers together, and all the variables

(-108x^2)+1404x+189*1296x^2=0

Wy multiply elements

(-108x^2)+244944x^2+1404x=0

We get rid of parentheses

-108x^2+244944x^2+1404x=0

We add all the numbers together, and all the variables

244836x^2+1404x=0

a = 244836; b = 1404; c = 0;
Δ = b2-4ac
Δ = 14042-4·244836·0
Δ = 1971216
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1971216}=1404$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1404)-1404}{2*244836}=\frac{-2808}{489672}
=-13/2267
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1404)+1404}{2*244836}=\frac{0}{489672}
=0
$