-1/2g+13=3g

Solution for -1/2g+13=3g equation:

-1/2g+13=3g

We move all terms to the left:

-1/2g+13-(3g)=0


Domain of the equation: 2g!=0

g!=0/2

g!=0

g∈R


We add all the numbers together, and all the variables

-3g-1/2g+13=0

We multiply all the terms by the denominator


-3g*2g+13*2g-1=0

Wy multiply elements

-6g^2+26g-1=0

a = -6; b = 26; c = -1;
Δ = b2-4ac
Δ = 262-4·(-6)·(-1)
Δ = 652
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:

$\sqrt{\Delta}=\sqrt{652}=\sqrt{4*163}=\sqrt{4}*\sqrt{163}=2\sqrt{163}$
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(26)-2\sqrt{163}}{2*-6}=\frac{-26-2\sqrt{163}}{-12}
$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(26)+2\sqrt{163}}{2*-6}=\frac{-26+2\sqrt{163}}{-12}
$