(7k+1)(k-2)=0

Solution for (7k+1)(k-2)=0 equation:

(7k+1)(k-2)=0

We multiply parentheses ..

(+7k^2-14k+k-2)=0

We get rid of parentheses

7k^2-14k+k-2=0

We add all the numbers together, and all the variables

7k^2-13k-2=0

a = 7; b = -13; c = -2;
Δ = b2-4ac
Δ = -132-4·7·(-2)
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-15}{2*7}=\frac{-2}{14}
=-1/7
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+15}{2*7}=\frac{28}{14}
=2
$