1/5g+1/2=5/6g

Solution for 1/5g+1/2=5/6g equation:

1/5g+1/2=5/6g

We move all terms to the left:

1/5g+1/2-(5/6g)=0


Domain of the equation: 5g!=0

g!=0/5

g!=0

g∈R



Domain of the equation: 6g)!=0

g!=0/1

g!=0

g∈R


We add all the numbers together, and all the variables

1/5g-(+5/6g)+1/2=0

We get rid of parentheses

1/5g-5/6g+1/2=0

We calculate fractions


180g^2/120g^2+24g/120g^2+(-100g)/120g^2=0

We multiply all the terms by the denominator


180g^2+24g+(-100g)=0

We get rid of parentheses

180g^2+24g-100g=0

We add all the numbers together, and all the variables

180g^2-76g=0

a = 180; b = -76; c = 0;
Δ = b2-4ac
Δ = -762-4·180·0
Δ = 5776
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5776}=76$
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-76)-76}{2*180}=\frac{0}{360}
=0
$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-76)+76}{2*180}=\frac{152}{360}
=19/45
$