5/9g+10=1/6g+3

Solution for 5/9g+10=1/6g+3 equation:

5/9g+10=1/6g+3

We move all terms to the left:

5/9g+10-(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+10=0

We calculate fractions


30g/54g^2+(-9g)/54g^2-3+10=0

We add all the numbers together, and all the variables

30g/54g^2+(-9g)/54g^2+7=0

We multiply all the terms by the denominator


30g+(-9g)+7*54g^2=0

Wy multiply elements

378g^2+30g+(-9g)=0

We get rid of parentheses

378g^2+30g-9g=0

We add all the numbers together, and all the variables

378g^2+21g=0

a = 378; b = 21; c = 0;
Δ = b2-4ac
Δ = 212-4·378·0
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-21}{2*378}=\frac{-42}{756}
=-1/18
$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+21}{2*378}=\frac{0}{756}
=0
$