20=0.0052s(0.0052s)+0.13s

Solution for 20=0.0052s(0.0052s)+0.13s equation:

20=0.0052s(0.0052s)+0.13s

We move all terms to the left:

20-(0.0052s(0.0052s)+0.13s)=0

We add all the numbers together, and all the variables

-(0.0052s(+0.0052s)+0.13s)+20=0


We calculate terms in parentheses: -(0.0052s(+0.0052s)+0.13s), so:

0.0052s(+0.0052s)+0.13s

We add all the numbers together, and all the variables

0.13s+0.0052s(+0.0052s)

We multiply parentheses

0s^2+0.13s

We add all the numbers together, and all the variables

s^2+0.13s

Back to the equation:

-(s^2+0.13s)


We get rid of parentheses

-s^2-0.13s+20=0

We add all the numbers together, and all the variables

-1s^2-0.13s+20=0

a = -1; b = -0.13; c = +20;
Δ = b2-4ac
Δ = -0.132-4·(-1)·20
Δ = 80.0169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-0.13)-\sqrt{80.0169}}{2*-1}=\frac{0.13-\sqrt{80.0169}}{-2}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-0.13)+\sqrt{80.0169}}{2*-1}=\frac{0.13+\sqrt{80.0169}}{-2}
$