9z-16/6z=14

Solution for 9z-16/6z=14 equation:

9z-16/6z=14

We move all terms to the left:

9z-16/6z-(14)=0


Domain of the equation: 6z!=0

z!=0/6

z!=0

z∈R


We multiply all the terms by the denominator


9z*6z-14*6z-16=0

Wy multiply elements

54z^2-84z-16=0

a = 54; b = -84; c = -16;
Δ = b2-4ac
Δ = -842-4·54·(-16)
Δ = 10512
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:

$\sqrt{\Delta}=\sqrt{10512}=\sqrt{144*73}=\sqrt{144}*\sqrt{73}=12\sqrt{73}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-84)-12\sqrt{73}}{2*54}=\frac{84-12\sqrt{73}}{108}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-84)+12\sqrt{73}}{2*54}=\frac{84+12\sqrt{73}}{108}
$