-2k(k-5)+2k=5k+5

Solution for -2k(k-5)+2k=5k+5 equation:

-2k(k-5)+2k=5k+5

We move all terms to the left:

-2k(k-5)+2k-(5k+5)=0

We add all the numbers together, and all the variables

2k-2k(k-5)-(5k+5)=0

We multiply parentheses

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-2k^2+7k-5=0

a = -2; b = 7; c = -5;
Δ = b2-4ac
Δ = 72-4·(-2)·(-5)
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-3}{2*-2}=\frac{-10}{-4}
=2+1/2
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+3}{2*-2}=\frac{-4}{-4}
=1
$