5/8g+8=1/6g+1

Solution for 5/8g+8=1/6g+1 equation:

5/8g+8=1/6g+1

We move all terms to the left:

5/8g+8-(1/6g+1)=0


Domain of the equation: 8g!=0

g!=0/8

g!=0

g∈R



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

g∈R


We get rid of parentheses

5/8g-1/6g-1+8=0

We calculate fractions


30g/48g^2+(-8g)/48g^2-1+8=0

We add all the numbers together, and all the variables

30g/48g^2+(-8g)/48g^2+7=0

We multiply all the terms by the denominator


30g+(-8g)+7*48g^2=0

Wy multiply elements

336g^2+30g+(-8g)=0

We get rid of parentheses

336g^2+30g-8g=0

We add all the numbers together, and all the variables

336g^2+22g=0

a = 336; b = 22; c = 0;
Δ = b2-4ac
Δ = 222-4·336·0
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-22}{2*336}=\frac{-44}{672}
=-11/168
$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+22}{2*336}=\frac{0}{672}
=0
$