(-41/2)z=-18

Solution for (-41/2)z=-18 equation:

(-41/2)z=-18

We move all terms to the left:

(-41/2)z-(-18)=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

(-41/2)z+18=0

We multiply parentheses

-41z^2+18=0

a = -41; b = 0; c = +18;
Δ = b2-4ac
Δ = 02-4·(-41)·18
Δ = 2952
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:

$\sqrt{\Delta}=\sqrt{2952}=\sqrt{36*82}=\sqrt{36}*\sqrt{82}=6\sqrt{82}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{82}}{2*-41}=\frac{0-6\sqrt{82}}{-82}
=-\frac{6\sqrt{82}}{-82}
=-\frac{3\sqrt{82}}{-41}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{82}}{2*-41}=\frac{0+6\sqrt{82}}{-82}
=\frac{6\sqrt{82}}{-82}
=\frac{3\sqrt{82}}{-41}
$