2k(k+45)=180

Solution for 2k(k+45)=180 equation:

2k(k+45)=180

We move all terms to the left:

2k(k+45)-(180)=0

We multiply parentheses

2k^2+90k-180=0

a = 2; b = 90; c = -180;
Δ = b2-4ac
Δ = 902-4·2·(-180)
Δ = 9540
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:

$\sqrt{\Delta}=\sqrt{9540}=\sqrt{36*265}=\sqrt{36}*\sqrt{265}=6\sqrt{265}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(90)-6\sqrt{265}}{2*2}=\frac{-90-6\sqrt{265}}{4}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(90)+6\sqrt{265}}{2*2}=\frac{-90+6\sqrt{265}}{4}
$