1/3g-5/6g=-10-2

Solution for 1/3g-5/6g=-10-2 equation:

1/3g-5/6g=-10-2

We move all terms to the left:

1/3g-5/6g-(-10-2)=0


Domain of the equation: 3g!=0

g!=0/3

g!=0

g∈R



Domain of the equation: 6g!=0

g!=0/6

g!=0

g∈R


We add all the numbers together, and all the variables

1/3g-5/6g-(-12)=0

We add all the numbers together, and all the variables

1/3g-5/6g+12=0

We calculate fractions


6g/18g^2+(-15g)/18g^2+12=0

We multiply all the terms by the denominator


6g+(-15g)+12*18g^2=0

Wy multiply elements

216g^2+6g+(-15g)=0

We get rid of parentheses

216g^2+6g-15g=0

We add all the numbers together, and all the variables

216g^2-9g=0

a = 216; b = -9; c = 0;
Δ = b2-4ac
Δ = -92-4·216·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-9}{2*216}=\frac{0}{432}
=0
$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+9}{2*216}=\frac{18}{432}
=1/24
$