5k^2+32k-12=0

Solution for 5k^2+32k-12=0 equation:

5k^2+32k-12=0

a = 5; b = 32; c = -12;
Δ = b2-4ac
Δ = 322-4·5·(-12)
Δ = 1264
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:

$\sqrt{\Delta}=\sqrt{1264}=\sqrt{16*79}=\sqrt{16}*\sqrt{79}=4\sqrt{79}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-4\sqrt{79}}{2*5}=\frac{-32-4\sqrt{79}}{10}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+4\sqrt{79}}{2*5}=\frac{-32+4\sqrt{79}}{10}
$