4k^2-4k-25=0

Solution for 4k^2-4k-25=0 equation:

4k^2-4k-25=0

a = 4; b = -4; c = -25;
Δ = b2-4ac
Δ = -42-4·4·(-25)
Δ = 416
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:

$\sqrt{\Delta}=\sqrt{416}=\sqrt{16*26}=\sqrt{16}*\sqrt{26}=4\sqrt{26}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{26}}{2*4}=\frac{4-4\sqrt{26}}{8}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{26}}{2*4}=\frac{4+4\sqrt{26}}{8}
$