19z-7/17z-5=1

Solution for 19z-7/17z-5=1 equation:

19z-7/17z-5=1

We move all terms to the left:

19z-7/17z-5-(1)=0


Domain of the equation: 17z!=0

z!=0/17

z!=0

z∈R


We add all the numbers together, and all the variables

19z-7/17z-6=0

We multiply all the terms by the denominator


19z*17z-6*17z-7=0

Wy multiply elements

323z^2-102z-7=0

a = 323; b = -102; c = -7;
Δ = b2-4ac
Δ = -1022-4·323·(-7)
Δ = 19448
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:

$\sqrt{\Delta}=\sqrt{19448}=\sqrt{4*4862}=\sqrt{4}*\sqrt{4862}=2\sqrt{4862}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-102)-2\sqrt{4862}}{2*323}=\frac{102-2\sqrt{4862}}{646}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-102)+2\sqrt{4862}}{2*323}=\frac{102+2\sqrt{4862}}{646}
$