1/10s+1/4s=21

Solution for 1/10s+1/4s=21 equation:

1/10s+1/4s=21

We move all terms to the left:

1/10s+1/4s-(21)=0


Domain of the equation: 10s!=0

s!=0/10

s!=0

s∈R



Domain of the equation: 4s!=0

s!=0/4

s!=0

s∈R


We calculate fractions


4s/40s^2+10s/40s^2-21=0

We multiply all the terms by the denominator


4s+10s-21*40s^2=0

We add all the numbers together, and all the variables

14s-21*40s^2=0

Wy multiply elements

-840s^2+14s=0

a = -840; b = 14; c = 0;
Δ = b2-4ac
Δ = 142-4·(-840)·0
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-14}{2*-840}=\frac{-28}{-1680}
=1/60
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+14}{2*-840}=\frac{0}{-1680}
=0
$