5k^2-40k=10

Solution for 5k^2-40k=10 equation:

5k^2-40k=10

We move all terms to the left:

5k^2-40k-(10)=0

a = 5; b = -40; c = -10;
Δ = b2-4ac
Δ = -402-4·5·(-10)
Δ = 1800
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:

$\sqrt{\Delta}=\sqrt{1800}=\sqrt{900*2}=\sqrt{900}*\sqrt{2}=30\sqrt{2}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-30\sqrt{2}}{2*5}=\frac{40-30\sqrt{2}}{10}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+30\sqrt{2}}{2*5}=\frac{40+30\sqrt{2}}{10}
$