9z^2+74=54z

Solution for 9z^2+74=54z equation:

9z^2+74=54z

We move all terms to the left:

9z^2+74-(54z)=0

a = 9; b = -54; c = +74;
Δ = b2-4ac
Δ = -542-4·9·74
Δ = 252
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{252}=\sqrt{36*7}=\sqrt{36}*\sqrt{7}=6\sqrt{7}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-54)-6\sqrt{7}}{2*9}=\frac{54-6\sqrt{7}}{18}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-54)+6\sqrt{7}}{2*9}=\frac{54+6\sqrt{7}}{18}
$