3g=(1/3)(50-g)

Solution for 3g=(1/3)(50-g) equation:

3g=(1/3)(50-g)

We move all terms to the left:

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


Domain of the equation: 3)(50-g))!=0

g∈R


We add all the numbers together, and all the variables

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

We multiply parentheses ..

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

We multiply all the terms by the denominator


-((-1g^2+1+3g*3*50))=0


We calculate terms in parentheses: -((-1g^2+1+3g*3*50)), so:

(-1g^2+1+3g*3*50)

We get rid of parentheses

-1g^2+3g*3*50+1

Wy multiply elements

-1g^2+450g*5+1

Wy multiply elements

-1g^2+2250g+1

Back to the equation:

-(-1g^2+2250g+1)


We get rid of parentheses

1g^2-2250g-1=0

We add all the numbers together, and all the variables

g^2-2250g-1=0

a = 1; b = -2250; c = -1;
Δ = b2-4ac
Δ = -22502-4·1·(-1)
Δ = 5062504
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{5062504}=\sqrt{4*1265626}=\sqrt{4}*\sqrt{1265626}=2\sqrt{1265626}$
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2250)-2\sqrt{1265626}}{2*1}=\frac{2250-2\sqrt{1265626}}{2}
$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2250)+2\sqrt{1265626}}{2*1}=\frac{2250+2\sqrt{1265626}}{2}
$