(-41/4)z=-17

Solution for (-41/4)z=-17 equation:

(-41/4)z=-17

We move all terms to the left:

(-41/4)z-(-17)=0


Domain of the equation: 4)z!=0

z!=0/1

z!=0

z∈R


We add all the numbers together, and all the variables

(-41/4)z+17=0

We multiply parentheses

-41z^2+17=0

a = -41; b = 0; c = +17;
Δ = b2-4ac
Δ = 02-4·(-41)·17
Δ = 2788
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:

$\sqrt{\Delta}=\sqrt{2788}=\sqrt{4*697}=\sqrt{4}*\sqrt{697}=2\sqrt{697}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{697}}{2*-41}=\frac{0-2\sqrt{697}}{-82}
=-\frac{2\sqrt{697}}{-82}
=-\frac{\sqrt{697}}{-41}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{697}}{2*-41}=\frac{0+2\sqrt{697}}{-82}
=\frac{2\sqrt{697}}{-82}
=\frac{\sqrt{697}}{-41}
$