1/5s+s=12

Solution for 1/5s+s=12 equation:

1/5s+s=12

We move all terms to the left:

1/5s+s-(12)=0


Domain of the equation: 5s!=0

s!=0/5

s!=0

s∈R


We add all the numbers together, and all the variables

s+1/5s-12=0

We multiply all the terms by the denominator


s*5s-12*5s+1=0

Wy multiply elements

5s^2-60s+1=0

a = 5; b = -60; c = +1;
Δ = b2-4ac
Δ = -602-4·5·1
Δ = 3580
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{3580}=\sqrt{4*895}=\sqrt{4}*\sqrt{895}=2\sqrt{895}$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-2\sqrt{895}}{2*5}=\frac{60-2\sqrt{895}}{10}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+2\sqrt{895}}{2*5}=\frac{60+2\sqrt{895}}{10}
$