45k^2+165k=90

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

45k^2+165k=90

We move all terms to the left:

45k^2+165k-(90)=0

a = 45; b = 165; c = -90;
Δ = b2-4ac
Δ = 1652-4·45·(-90)
Δ = 43425
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:

$\sqrt{\Delta}=\sqrt{43425}=\sqrt{225*193}=\sqrt{225}*\sqrt{193}=15\sqrt{193}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(165)-15\sqrt{193}}{2*45}=\frac{-165-15\sqrt{193}}{90}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(165)+15\sqrt{193}}{2*45}=\frac{-165+15\sqrt{193}}{90}
$