(15/8)z+1/4=4

Solution for (15/8)z+1/4=4 equation:

(15/8)z+1/4=4

We move all terms to the left:

(15/8)z+1/4-(4)=0


Domain of the equation: 8)z!=0

z!=0/1

z!=0

z∈R


determiningTheFunctionDomain
(15/8)z-4+1/4=0

We add all the numbers together, and all the variables

(+15/8)z-4+1/4=0

We multiply parentheses

15z^2-4+1/4=0

We multiply all the terms by the denominator


15z^2*4+1-4*4=0

We add all the numbers together, and all the variables

15z^2*4-15=0

Wy multiply elements

60z^2-15=0

a = 60; b = 0; c = -15;
Δ = b2-4ac
Δ = 02-4·60·(-15)
Δ = 3600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3600}=60$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-60}{2*60}=\frac{-60}{120}
=-1/2
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+60}{2*60}=\frac{60}{120}
=1/2
$