9k^2-55=-14k

Solution for 9k^2-55=-14k equation:

9k^2-55=-14k

We move all terms to the left:

9k^2-55-(-14k)=0

We get rid of parentheses

9k^2+14k-55=0

a = 9; b = 14; c = -55;
Δ = b2-4ac
Δ = 142-4·9·(-55)
Δ = 2176
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:

$\sqrt{\Delta}=\sqrt{2176}=\sqrt{64*34}=\sqrt{64}*\sqrt{34}=8\sqrt{34}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-8\sqrt{34}}{2*9}=\frac{-14-8\sqrt{34}}{18}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+8\sqrt{34}}{2*9}=\frac{-14+8\sqrt{34}}{18}
$