9z-5/4z=-5

Solution for 9z-5/4z=-5 equation:

9z-5/4z=-5

We move all terms to the left:

9z-5/4z-(-5)=0


Domain of the equation: 4z!=0

z!=0/4

z!=0

z∈R


We add all the numbers together, and all the variables

9z-5/4z+5=0

We multiply all the terms by the denominator


9z*4z+5*4z-5=0

Wy multiply elements

36z^2+20z-5=0

a = 36; b = 20; c = -5;
Δ = b2-4ac
Δ = 202-4·36·(-5)
Δ = 1120
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:

$\sqrt{\Delta}=\sqrt{1120}=\sqrt{16*70}=\sqrt{16}*\sqrt{70}=4\sqrt{70}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-4\sqrt{70}}{2*36}=\frac{-20-4\sqrt{70}}{72}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+4\sqrt{70}}{2*36}=\frac{-20+4\sqrt{70}}{72}
$