40k^2-90k-90=0

Solution for 40k^2-90k-90=0 equation:

40k^2-90k-90=0

a = 40; b = -90; c = -90;
Δ = b2-4ac
Δ = -902-4·40·(-90)
Δ = 22500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{22500}=150$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-90)-150}{2*40}=\frac{-60}{80}
=-3/4
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-90)+150}{2*40}=\frac{240}{80}
=3
$