9/10z-2=9/20z+3

Solution for 9/10z-2=9/20z+3 equation:

9/10z-2=9/20z+3

We move all terms to the left:

9/10z-2-(9/20z+3)=0


Domain of the equation: 10z!=0

z!=0/10

z!=0

z∈R



Domain of the equation: 20z+3)!=0

z∈R


We get rid of parentheses

9/10z-9/20z-3-2=0

We calculate fractions


180z/200z^2+(-90z)/200z^2-3-2=0

We add all the numbers together, and all the variables

180z/200z^2+(-90z)/200z^2-5=0

We multiply all the terms by the denominator


180z+(-90z)-5*200z^2=0

Wy multiply elements

-1000z^2+180z+(-90z)=0

We get rid of parentheses

-1000z^2+180z-90z=0

We add all the numbers together, and all the variables

-1000z^2+90z=0

a = -1000; b = 90; c = 0;
Δ = b2-4ac
Δ = 902-4·(-1000)·0
Δ = 8100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{8100}=90$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(90)-90}{2*-1000}=\frac{-180}{-2000}
=9/100
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(90)+90}{2*-1000}=\frac{0}{-2000}
=0
$