1/5z+3=-z+21

Solution for 1/5z+3=-z+21 equation:

1/5z+3=-z+21

We move all terms to the left:

1/5z+3-(-z+21)=0


Domain of the equation: 5z!=0

z!=0/5

z!=0

z∈R


We add all the numbers together, and all the variables

1/5z-(-1z+21)+3=0

We get rid of parentheses

1/5z+1z-21+3=0

We multiply all the terms by the denominator


1z*5z-21*5z+3*5z+1=0

Wy multiply elements

5z^2-105z+15z+1=0

We add all the numbers together, and all the variables

5z^2-90z+1=0

a = 5; b = -90; c = +1;
Δ = b2-4ac
Δ = -902-4·5·1
Δ = 8080
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:

$\sqrt{\Delta}=\sqrt{8080}=\sqrt{16*505}=\sqrt{16}*\sqrt{505}=4\sqrt{505}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-90)-4\sqrt{505}}{2*5}=\frac{90-4\sqrt{505}}{10}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-90)+4\sqrt{505}}{2*5}=\frac{90+4\sqrt{505}}{10}
$