7k+8-9k2-5k=0

Solution for 7k+8-9k2-5k=0 equation:

7k+8-9k^2-5k=0

We add all the numbers together, and all the variables

-9k^2+2k+8=0

a = -9; b = 2; c = +8;
Δ = b2-4ac
Δ = 22-4·(-9)·8
Δ = 292
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:

$\sqrt{\Delta}=\sqrt{292}=\sqrt{4*73}=\sqrt{4}*\sqrt{73}=2\sqrt{73}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{73}}{2*-9}=\frac{-2-2\sqrt{73}}{-18}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{73}}{2*-9}=\frac{-2+2\sqrt{73}}{-18}
$