4/9g+8=1/6g+1

Solution for 4/9g+8=1/6g+1 equation:

4/9g+8=1/6g+1

We move all terms to the left:

4/9g+8-(1/6g+1)=0


Domain of the equation: 9g!=0

g!=0/9

g!=0

g∈R



Domain of the equation: 6g+1)!=0

g∈R


We get rid of parentheses

4/9g-1/6g-1+8=0

We calculate fractions


24g/54g^2+(-9g)/54g^2-1+8=0

We add all the numbers together, and all the variables

24g/54g^2+(-9g)/54g^2+7=0

We multiply all the terms by the denominator


24g+(-9g)+7*54g^2=0

Wy multiply elements

378g^2+24g+(-9g)=0

We get rid of parentheses

378g^2+24g-9g=0

We add all the numbers together, and all the variables

378g^2+15g=0

a = 378; b = 15; c = 0;
Δ = b2-4ac
Δ = 152-4·378·0
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-15}{2*378}=\frac{-30}{756}
=-5/126
$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+15}{2*378}=\frac{0}{756}
=0
$