150-1/2s=120+1/4s

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

150-1/2s=120+1/4s

We move all terms to the left:

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


Domain of the equation: 2s!=0

s!=0/2

s!=0

s∈R



Domain of the equation: 4s)!=0

s!=0/1

s!=0

s∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


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

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We get rid of parentheses

240s^2-4s-2s=0

We add all the numbers together, and all the variables

240s^2-6s=0

a = 240; b = -6; c = 0;
Δ = b2-4ac
Δ = -62-4·240·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6}{2*240}=\frac{0}{480}
=0
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6}{2*240}=\frac{12}{480}
=1/40
$