60=1/4g+12;g=12

Solution for 60=1/4g+12;g=12 equation:

60=1/4g+12g=12

We move all terms to the left:

60-(1/4g+12g)=0


Domain of the equation: 4g+12g)!=0

g∈R


We add all the numbers together, and all the variables

-(+12g+1/4g)+60=0

We get rid of parentheses

-12g-1/4g+60=0

We multiply all the terms by the denominator


-12g*4g+60*4g-1=0

Wy multiply elements

-48g^2+240g-1=0

a = -48; b = 240; c = -1;
Δ = b2-4ac
Δ = 2402-4·(-48)·(-1)
Δ = 57408
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:

$\sqrt{\Delta}=\sqrt{57408}=\sqrt{64*897}=\sqrt{64}*\sqrt{897}=8\sqrt{897}$
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(240)-8\sqrt{897}}{2*-48}=\frac{-240-8\sqrt{897}}{-96}
$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(240)+8\sqrt{897}}{2*-48}=\frac{-240+8\sqrt{897}}{-96}
$