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

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

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

We move all terms to the left:

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


Domain of the equation: 2s!=0

s!=0/2

s!=0

s∈R



Domain of the equation: 4s!=0

s!=0/4

s!=0

s∈R


We add all the numbers together, and all the variables

1/2s-1/4s+7=0

We calculate fractions


4s/8s^2+(-2s)/8s^2+7=0

We multiply all the terms by the denominator


4s+(-2s)+7*8s^2=0

Wy multiply elements

56s^2+4s+(-2s)=0

We get rid of parentheses

56s^2+4s-2s=0

We add all the numbers together, and all the variables

56s^2+2s=0

a = 56; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·56·0
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*56}=\frac{-4}{112}
=-1/28
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2}{2*56}=\frac{0}{112}
=0
$