(2/3)g+(1/2)g=14

Solution for (2/3)g+(1/2)g=14 equation:

(2/3)g+(1/2)g=14

We move all terms to the left:

(2/3)g+(1/2)g-(14)=0


Domain of the equation: 3)g!=0

g!=0/1

g!=0

g∈R



Domain of the equation: 2)g!=0

g!=0/1

g!=0

g∈R


We add all the numbers together, and all the variables

(+2/3)g+(+1/2)g-14=0

We multiply parentheses

2g^2+g^2-14=0

We add all the numbers together, and all the variables

3g^2-14=0

a = 3; b = 0; c = -14;
Δ = b2-4ac
Δ = 02-4·3·(-14)
Δ = 168
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:

$\sqrt{\Delta}=\sqrt{168}=\sqrt{4*42}=\sqrt{4}*\sqrt{42}=2\sqrt{42}$
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{42}}{2*3}=\frac{0-2\sqrt{42}}{6}
=-\frac{2\sqrt{42}}{6}
=-\frac{\sqrt{42}}{3}
$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{42}}{2*3}=\frac{0+2\sqrt{42}}{6}
=\frac{2\sqrt{42}}{6}
=\frac{\sqrt{42}}{3}
$