4/5*z=1

Solution for 4/5*z=1 equation:

4/5*z=1

We move all terms to the left:

4/5*z-(1)=0


Domain of the equation: 5*z!=0

z!=0/1

z!=0

z∈R


We multiply all the terms by the denominator


-1*5*z+4=0

Wy multiply elements

-5z*z+4=0

Wy multiply elements

-5z^2+4=0

a = -5; b = 0; c = +4;
Δ = b2-4ac
Δ = 02-4·(-5)·4
Δ = 80
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:

$\sqrt{\Delta}=\sqrt{80}=\sqrt{16*5}=\sqrt{16}*\sqrt{5}=4\sqrt{5}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{5}}{2*-5}=\frac{0-4\sqrt{5}}{-10}
=-\frac{4\sqrt{5}}{-10}
=-\frac{2\sqrt{5}}{-5}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{5}}{2*-5}=\frac{0+4\sqrt{5}}{-10}
=\frac{4\sqrt{5}}{-10}
=\frac{2\sqrt{5}}{-5}
$