9/10z-4=-19/20z+1

Solution for 9/10z-4=-19/20z+1 equation:

9/10z-4=-19/20z+1

We move all terms to the left:

9/10z-4-(-19/20z+1)=0


Domain of the equation: 10z!=0

z!=0/10

z!=0

z∈R



Domain of the equation: 20z+1)!=0

z∈R


We get rid of parentheses

9/10z+19/20z-1-4=0

We calculate fractions


180z/200z^2+190z/200z^2-1-4=0

We add all the numbers together, and all the variables

180z/200z^2+190z/200z^2-5=0

We multiply all the terms by the denominator


180z+190z-5*200z^2=0

We add all the numbers together, and all the variables

370z-5*200z^2=0

Wy multiply elements

-1000z^2+370z=0

a = -1000; b = 370; c = 0;
Δ = b2-4ac
Δ = 3702-4·(-1000)·0
Δ = 136900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{136900}=370$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(370)-370}{2*-1000}=\frac{-740}{-2000}
=37/100
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(370)+370}{2*-1000}=\frac{0}{-2000}
=0
$