(21/4)z+44=64

Solution for (21/4)z+44=64 equation:

(21/4)z+44=64

We move all terms to the left:

(21/4)z+44-(64)=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

(+21/4)z+44-64=0

We add all the numbers together, and all the variables

(+21/4)z-20=0

We multiply parentheses

21z^2-20=0

a = 21; b = 0; c = -20;
Δ = b2-4ac
Δ = 02-4·21·(-20)
Δ = 1680
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:

$\sqrt{\Delta}=\sqrt{1680}=\sqrt{16*105}=\sqrt{16}*\sqrt{105}=4\sqrt{105}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{105}}{2*21}=\frac{0-4\sqrt{105}}{42}
=-\frac{4\sqrt{105}}{42}
=-\frac{2\sqrt{105}}{21}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{105}}{2*21}=\frac{0+4\sqrt{105}}{42}
=\frac{4\sqrt{105}}{42}
=\frac{2\sqrt{105}}{21}
$