1/10g=12g

Solution for 1/10g=12g equation:

1/10g=12g

We move all terms to the left:

1/10g-(12g)=0


Domain of the equation: 10g!=0

g!=0/10

g!=0

g∈R


We add all the numbers together, and all the variables

-12g+1/10g=0

We multiply all the terms by the denominator


-12g*10g+1=0

Wy multiply elements

-120g^2+1=0

a = -120; b = 0; c = +1;
Δ = b2-4ac
Δ = 02-4·(-120)·1
Δ = 480
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:

$\sqrt{\Delta}=\sqrt{480}=\sqrt{16*30}=\sqrt{16}*\sqrt{30}=4\sqrt{30}$
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{30}}{2*-120}=\frac{0-4\sqrt{30}}{-240}
=-\frac{4\sqrt{30}}{-240}
=-\frac{\sqrt{30}}{-60}
$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{30}}{2*-120}=\frac{0+4\sqrt{30}}{-240}
=\frac{4\sqrt{30}}{-240}
=\frac{\sqrt{30}}{-60}
$