8k^2+31k-13=0

Solution for 8k^2+31k-13=0 equation:

8k^2+31k-13=0

a = 8; b = 31; c = -13;
Δ = b2-4ac
Δ = 312-4·8·(-13)
Δ = 1377
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:

$\sqrt{\Delta}=\sqrt{1377}=\sqrt{81*17}=\sqrt{81}*\sqrt{17}=9\sqrt{17}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(31)-9\sqrt{17}}{2*8}=\frac{-31-9\sqrt{17}}{16}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(31)+9\sqrt{17}}{2*8}=\frac{-31+9\sqrt{17}}{16}
$