10k^2-5=5k

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

10k^2-5=5k

We move all terms to the left:

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

a = 10; b = -5; c = -5;
Δ = b2-4ac
Δ = -52-4·10·(-5)
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-15}{2*10}=\frac{-10}{20}
=-1/2
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+15}{2*10}=\frac{20}{20}
=1
$