-7k^2+18k-9=0

Solution for -7k^2+18k-9=0 equation:

-7k^2+18k-9=0

a = -7; b = 18; c = -9;
Δ = b2-4ac
Δ = 182-4·(-7)·(-9)
Δ = 72
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:

$\sqrt{\Delta}=\sqrt{72}=\sqrt{36*2}=\sqrt{36}*\sqrt{2}=6\sqrt{2}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-6\sqrt{2}}{2*-7}=\frac{-18-6\sqrt{2}}{-14}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+6\sqrt{2}}{2*-7}=\frac{-18+6\sqrt{2}}{-14}
$