100k^2+10=47

Solution for 100k^2+10=47 equation:

100k^2+10=47

We move all terms to the left:

100k^2+10-(47)=0

We add all the numbers together, and all the variables

100k^2-37=0

a = 100; b = 0; c = -37;
Δ = b2-4ac
Δ = 02-4·100·(-37)
Δ = 14800
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{14800}=\sqrt{400*37}=\sqrt{400}*\sqrt{37}=20\sqrt{37}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-20\sqrt{37}}{2*100}=\frac{0-20\sqrt{37}}{200}
=-\frac{20\sqrt{37}}{200}
=-\frac{\sqrt{37}}{10}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+20\sqrt{37}}{2*100}=\frac{0+20\sqrt{37}}{200}
=\frac{20\sqrt{37}}{200}
=\frac{\sqrt{37}}{10}
$