1/4s=4s-21

Solution for 1/4s=4s-21 equation:

1/4s=4s-21

We move all terms to the left:

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


Domain of the equation: 4s!=0

s!=0/4

s!=0

s∈R


We get rid of parentheses

1/4s-4s+21=0

We multiply all the terms by the denominator


-4s*4s+21*4s+1=0

Wy multiply elements

-16s^2+84s+1=0

a = -16; b = 84; c = +1;
Δ = b2-4ac
Δ = 842-4·(-16)·1
Δ = 7120
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:

$\sqrt{\Delta}=\sqrt{7120}=\sqrt{16*445}=\sqrt{16}*\sqrt{445}=4\sqrt{445}$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(84)-4\sqrt{445}}{2*-16}=\frac{-84-4\sqrt{445}}{-32}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(84)+4\sqrt{445}}{2*-16}=\frac{-84+4\sqrt{445}}{-32}
$