(5k+1)(5k+10)=9*180

Solution for (5k+1)(5k+10)=9*180 equation:

(5k+1)(5k+10)=9*180

We move all terms to the left:

(5k+1)(5k+10)-(9*180)=0

We add all the numbers together, and all the variables

(5k+1)(5k+10)-1620=0

We multiply parentheses ..

(+25k^2+50k+5k+10)-1620=0

We get rid of parentheses

25k^2+50k+5k+10-1620=0

We add all the numbers together, and all the variables

25k^2+55k-1610=0

a = 25; b = 55; c = -1610;
Δ = b2-4ac
Δ = 552-4·25·(-1610)
Δ = 164025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{164025}=405$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(55)-405}{2*25}=\frac{-460}{50}
=-9+1/5
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(55)+405}{2*25}=\frac{350}{50}
=7
$