1/3g+1/2g=50

Solution for 1/3g+1/2g=50 equation:

1/3g+1/2g=50

We move all terms to the left:

1/3g+1/2g-(50)=0


Domain of the equation: 3g!=0

g!=0/3

g!=0

g∈R



Domain of the equation: 2g!=0

g!=0/2

g!=0

g∈R


We calculate fractions


2g/6g^2+3g/6g^2-50=0

We multiply all the terms by the denominator


2g+3g-50*6g^2=0

We add all the numbers together, and all the variables

5g-50*6g^2=0

Wy multiply elements

-300g^2+5g=0

a = -300; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·(-300)·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5}{2*-300}=\frac{-10}{-600}
=1/60
$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*-300}=\frac{0}{-600}
=0
$