5k^2-31k-72=0

Solution for 5k^2-31k-72=0 equation:

5k^2-31k-72=0

a = 5; b = -31; c = -72;
Δ = b2-4ac
Δ = -312-4·5·(-72)
Δ = 2401
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2401}=49$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-31)-49}{2*5}=\frac{-18}{10}
=-1+4/5
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-31)+49}{2*5}=\frac{80}{10}
=8
$