1/10z+3/5z=-21

Solution for 1/10z+3/5z=-21 equation:

1/10z+3/5z=-21

We move all terms to the left:

1/10z+3/5z-(-21)=0


Domain of the equation: 10z!=0

z!=0/10

z!=0

z∈R



Domain of the equation: 5z!=0

z!=0/5

z!=0

z∈R


We add all the numbers together, and all the variables

1/10z+3/5z+21=0

We calculate fractions


5z/50z^2+30z/50z^2+21=0

We multiply all the terms by the denominator


5z+30z+21*50z^2=0

We add all the numbers together, and all the variables

35z+21*50z^2=0

Wy multiply elements

1050z^2+35z=0

a = 1050; b = 35; c = 0;
Δ = b2-4ac
Δ = 352-4·1050·0
Δ = 1225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1225}=35$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(35)-35}{2*1050}=\frac{-70}{2100}
=-1/30
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(35)+35}{2*1050}=\frac{0}{2100}
=0
$