k2+65k-720=0

Solution for k2+65k-720=0 equation:

k2+65k-720=0

We add all the numbers together, and all the variables

k^2+65k-720=0

a = 1; b = 65; c = -720;
Δ = b2-4ac
Δ = 652-4·1·(-720)
Δ = 7105
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:

$\sqrt{\Delta}=\sqrt{7105}=\sqrt{49*145}=\sqrt{49}*\sqrt{145}=7\sqrt{145}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(65)-7\sqrt{145}}{2*1}=\frac{-65-7\sqrt{145}}{2}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(65)+7\sqrt{145}}{2*1}=\frac{-65+7\sqrt{145}}{2}
$