8k+10-4k^2=0

Solution for 8k+10-4k^2=0 equation:

8k+10-4k^2=0

a = -4; b = 8; c = +10;
Δ = b2-4ac
Δ = 82-4·(-4)·10
Δ = 224
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:

$\sqrt{\Delta}=\sqrt{224}=\sqrt{16*14}=\sqrt{16}*\sqrt{14}=4\sqrt{14}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-4\sqrt{14}}{2*-4}=\frac{-8-4\sqrt{14}}{-8}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+4\sqrt{14}}{2*-4}=\frac{-8+4\sqrt{14}}{-8}
$