9k2=23+10k

Solution for 9k2=23+10k equation:

9k^2=23+10k

We move all terms to the left:

9k^2-(23+10k)=0

We add all the numbers together, and all the variables

9k^2-(10k+23)=0

We get rid of parentheses

9k^2-10k-23=0

a = 9; b = -10; c = -23;
Δ = b2-4ac
Δ = -102-4·9·(-23)
Δ = 928
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:

$\sqrt{\Delta}=\sqrt{928}=\sqrt{16*58}=\sqrt{16}*\sqrt{58}=4\sqrt{58}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-4\sqrt{58}}{2*9}=\frac{10-4\sqrt{58}}{18}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+4\sqrt{58}}{2*9}=\frac{10+4\sqrt{58}}{18}
$