z^2-7z/2-72=0

Solution for z^2-7z/2-72=0 equation:

z^2-7z/2-72=0

We multiply all the terms by the denominator


z^2*2-7z-72*2=0

We add all the numbers together, and all the variables

z^2*2-7z-144=0

Wy multiply elements

2z^2-7z-144=0

a = 2; b = -7; c = -144;
Δ = b2-4ac
Δ = -72-4·2·(-144)
Δ = 1201
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-\sqrt{1201}}{2*2}=\frac{7-\sqrt{1201}}{4}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{1201}}{2*2}=\frac{7+\sqrt{1201}}{4}
$