1/2s-6=1/4s+4

Solution for 1/2s-6=1/4s+4 equation:

1/2s-6=1/4s+4

We move all terms to the left:

1/2s-6-(1/4s+4)=0


Domain of the equation: 2s!=0

s!=0/2

s!=0

s∈R



Domain of the equation: 4s+4)!=0

s∈R


We get rid of parentheses

1/2s-1/4s-4-6=0

We calculate fractions


4s/8s^2+(-2s)/8s^2-4-6=0

We add all the numbers together, and all the variables

4s/8s^2+(-2s)/8s^2-10=0

We multiply all the terms by the denominator


4s+(-2s)-10*8s^2=0

Wy multiply elements

-80s^2+4s+(-2s)=0

We get rid of parentheses

-80s^2+4s-2s=0

We add all the numbers together, and all the variables

-80s^2+2s=0

a = -80; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·(-80)·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2}{2*-80}=\frac{-4}{-160}
=1/40
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2}{2*-80}=\frac{0}{-160}
=0
$