5(4z)-1/2z=24

Solution for 5(4z)-1/2z=24 equation:

5(4z)-1/2z=24

We move all terms to the left:

5(4z)-1/2z-(24)=0


Domain of the equation: 2z!=0

z!=0/2

z!=0

z∈R


We multiply all the terms by the denominator


54z*2z-24*2z-1=0

Wy multiply elements

108z^2-48z-1=0

a = 108; b = -48; c = -1;
Δ = b2-4ac
Δ = -482-4·108·(-1)
Δ = 2736
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:

$\sqrt{\Delta}=\sqrt{2736}=\sqrt{144*19}=\sqrt{144}*\sqrt{19}=12\sqrt{19}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-12\sqrt{19}}{2*108}=\frac{48-12\sqrt{19}}{216}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+12\sqrt{19}}{2*108}=\frac{48+12\sqrt{19}}{216}
$