1/3g+1/7g=8

Solution for 1/3g+1/7g=8 equation:

1/3g+1/7g=8

We move all terms to the left:

1/3g+1/7g-(8)=0


Domain of the equation: 3g!=0

g!=0/3

g!=0

g∈R



Domain of the equation: 7g!=0

g!=0/7

g!=0

g∈R


We calculate fractions


7g/21g^2+3g/21g^2-8=0

We multiply all the terms by the denominator


7g+3g-8*21g^2=0

We add all the numbers together, and all the variables

10g-8*21g^2=0

Wy multiply elements

-168g^2+10g=0

a = -168; b = 10; c = 0;
Δ = b2-4ac
Δ = 102-4·(-168)·0
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-10}{2*-168}=\frac{-20}{-336}
=5/84
$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+10}{2*-168}=\frac{0}{-336}
=0
$