5/9g+185/9=1/6g+3

Solution for 5/9g+185/9=1/6g+3 equation:

5/9g+185/9=1/6g+3

We move all terms to the left:

5/9g+185/9-(1/6g+3)=0


Domain of the equation: 9g!=0

g!=0/9

g!=0

g∈R



Domain of the equation: 6g+3)!=0

g∈R


We get rid of parentheses

5/9g-1/6g-3+185/9=0

We calculate fractions


30g/4374g^2+(-729g)/4374g^2+1110g/4374g^2-3=0

We multiply all the terms by the denominator


30g+(-729g)+1110g-3*4374g^2=0

We add all the numbers together, and all the variables

1140g+(-729g)-3*4374g^2=0

Wy multiply elements

-13122g^2+1140g+(-729g)=0

We get rid of parentheses

-13122g^2+1140g-729g=0

We add all the numbers together, and all the variables

-13122g^2+411g=0

a = -13122; b = 411; c = 0;
Δ = b2-4ac
Δ = 4112-4·(-13122)·0
Δ = 168921
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{168921}=411$
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(411)-411}{2*-13122}=\frac{-822}{-26244}
=137/4374
$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(411)+411}{2*-13122}=\frac{0}{-26244}
=0
$