150+1/2g=120+1/4g

Solution for 150+1/2g=120+1/4g equation:

150+1/2g=120+1/4g

We move all terms to the left:

150+1/2g-(120+1/4g)=0


Domain of the equation: 2g!=0

g!=0/2

g!=0

g∈R



Domain of the equation: 4g)!=0

g!=0/1

g!=0

g∈R


We add all the numbers together, and all the variables

1/2g-(1/4g+120)+150=0

We get rid of parentheses

1/2g-1/4g-120+150=0

We calculate fractions


4g/8g^2+(-2g)/8g^2-120+150=0

We add all the numbers together, and all the variables

4g/8g^2+(-2g)/8g^2+30=0

We multiply all the terms by the denominator


4g+(-2g)+30*8g^2=0

Wy multiply elements

240g^2+4g+(-2g)=0

We get rid of parentheses

240g^2+4g-2g=0

We add all the numbers together, and all the variables

240g^2+2g=0

a = 240; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·240·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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