-5k^2-4K+5=5k-10k^2+10

Solution for -5k^2-4K+5=5k-10k^2+10 equation:

-5k^2-4+5=5k-10k^2+10

We move all terms to the left:

-5k^2-4+5-(5k-10k^2+10)=0

We add all the numbers together, and all the variables

-5k^2-(5k-10k^2+10)+1=0

We get rid of parentheses

-5k^2+10k^2-5k-10+1=0

We add all the numbers together, and all the variables

5k^2-5k-9=0

a = 5; b = -5; c = -9;
Δ = b2-4ac
Δ = -52-4·5·(-9)
Δ = 205
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{-(-5)-\sqrt{205}}{2*5}=\frac{5-\sqrt{205}}{10}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{205}}{2*5}=\frac{5+\sqrt{205}}{10}
$