5(4z)-1/2z=23

Solution for 5(4z)-1/2z=23 equation:

5(4z)-1/2z=23

We move all terms to the left:

5(4z)-1/2z-(23)=0


Domain of the equation: 2z!=0

z!=0/2

z!=0

z∈R


We multiply all the terms by the denominator


54z*2z-23*2z-1=0

Wy multiply elements

108z^2-46z-1=0

a = 108; b = -46; c = -1;
Δ = b2-4ac
Δ = -462-4·108·(-1)
Δ = 2548
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:

$\sqrt{\Delta}=\sqrt{2548}=\sqrt{196*13}=\sqrt{196}*\sqrt{13}=14\sqrt{13}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-46)-14\sqrt{13}}{2*108}=\frac{46-14\sqrt{13}}{216}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-46)+14\sqrt{13}}{2*108}=\frac{46+14\sqrt{13}}{216}
$