1/4g+12;g=12

Solution for 1/4g+12;g=12 equation:

1/4g+12g=12

We move all terms to the left:

1/4g+12g-(12)=0


Domain of the equation: 4g!=0

g!=0/4

g!=0

g∈R


We add all the numbers together, and all the variables

12g+1/4g-12=0

We multiply all the terms by the denominator


12g*4g-12*4g+1=0

Wy multiply elements

48g^2-48g+1=0

a = 48; b = -48; c = +1;
Δ = b2-4ac
Δ = -482-4·48·1
Δ = 2112
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:

$\sqrt{\Delta}=\sqrt{2112}=\sqrt{64*33}=\sqrt{64}*\sqrt{33}=8\sqrt{33}$
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-8\sqrt{33}}{2*48}=\frac{48-8\sqrt{33}}{96}
$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+8\sqrt{33}}{2*48}=\frac{48+8\sqrt{33}}{96}
$