45k^2+165k+90=0

Solution for 45k^2+165k+90=0 equation:

45k^2+165k+90=0

a = 45; b = 165; c = +90;
Δ = b2-4ac
Δ = 1652-4·45·90
Δ = 11025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{11025}=105$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(165)-105}{2*45}=\frac{-270}{90}
=-3
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(165)+105}{2*45}=\frac{-60}{90}
=-2/3
$