(5/2)*z-7=23

Solution for (5/2)*z-7=23 equation:

(5/2)*z-7=23

We move all terms to the left:

(5/2)*z-7-(23)=0


Domain of the equation: 2)*z!=0

z!=0/1

z!=0

z∈R


We add all the numbers together, and all the variables

(+5/2)*z-7-23=0

We add all the numbers together, and all the variables

(+5/2)*z-30=0

We multiply parentheses

5z^2-30=0

a = 5; b = 0; c = -30;
Δ = b2-4ac
Δ = 02-4·5·(-30)
Δ = 600
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:

$\sqrt{\Delta}=\sqrt{600}=\sqrt{100*6}=\sqrt{100}*\sqrt{6}=10\sqrt{6}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{6}}{2*5}=\frac{0-10\sqrt{6}}{10}
=-\frac{10\sqrt{6}}{10}
=-\sqrt{6}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{6}}{2*5}=\frac{0+10\sqrt{6}}{10}
=\frac{10\sqrt{6}}{10}
=\sqrt{6}
$