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

Solution for (5k^2+5k-5)=0 equation:

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

We get rid of parentheses

5k^2+5k-5=0

a = 5; b = 5; c = -5;
Δ = b2-4ac
Δ = 52-4·5·(-5)
Δ = 125
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:

$\sqrt{\Delta}=\sqrt{125}=\sqrt{25*5}=\sqrt{25}*\sqrt{5}=5\sqrt{5}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5\sqrt{5}}{2*5}=\frac{-5-5\sqrt{5}}{10}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5\sqrt{5}}{2*5}=\frac{-5+5\sqrt{5}}{10}
$