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

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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 $

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