5k^2-k-47=0

Solution for 5k^2-k-47=0 equation:

5k^2-k-47=0

We add all the numbers together, and all the variables

5k^2-1k-47=0

a = 5; b = -1; c = -47;
Δ = b2-4ac
Δ = -12-4·5·(-47)
Δ = 941
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-\sqrt{941}}{2*5}=\frac{1-\sqrt{941}}{10}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{941}}{2*5}=\frac{1+\sqrt{941}}{10}
$