7k2-12k-21=0

Solution for 7k2-12k-21=0 equation:

7k^2-12k-21=0

a = 7; b = -12; c = -21;
Δ = b2-4ac
Δ = -122-4·7·(-21)
Δ = 732
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:

$\sqrt{\Delta}=\sqrt{732}=\sqrt{4*183}=\sqrt{4}*\sqrt{183}=2\sqrt{183}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{183}}{2*7}=\frac{12-2\sqrt{183}}{14}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{183}}{2*7}=\frac{12+2\sqrt{183}}{14}
$