(5k-3)(9+k)=180

Solution for (5k-3)(9+k)=180 equation:

(5k-3)(9+k)=180

We move all terms to the left:

(5k-3)(9+k)-(180)=0

We add all the numbers together, and all the variables

(5k-3)(k+9)-180=0

We multiply parentheses ..

(+5k^2+45k-3k-27)-180=0

We get rid of parentheses

5k^2+45k-3k-27-180=0

We add all the numbers together, and all the variables

5k^2+42k-207=0

a = 5; b = 42; c = -207;
Δ = b2-4ac
Δ = 422-4·5·(-207)
Δ = 5904
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:

$\sqrt{\Delta}=\sqrt{5904}=\sqrt{144*41}=\sqrt{144}*\sqrt{41}=12\sqrt{41}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(42)-12\sqrt{41}}{2*5}=\frac{-42-12\sqrt{41}}{10}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(42)+12\sqrt{41}}{2*5}=\frac{-42+12\sqrt{41}}{10}
$