4/5z-4=-9/10z+1

Solution for 4/5z-4=-9/10z+1 equation:

4/5z-4=-9/10z+1

We move all terms to the left:

4/5z-4-(-9/10z+1)=0


Domain of the equation: 5z!=0

z!=0/5

z!=0

z∈R



Domain of the equation: 10z+1)!=0

z∈R


We get rid of parentheses

4/5z+9/10z-1-4=0

We calculate fractions


40z/50z^2+45z/50z^2-1-4=0

We add all the numbers together, and all the variables

40z/50z^2+45z/50z^2-5=0

We multiply all the terms by the denominator


40z+45z-5*50z^2=0

We add all the numbers together, and all the variables

85z-5*50z^2=0

Wy multiply elements

-250z^2+85z=0

a = -250; b = 85; c = 0;
Δ = b2-4ac
Δ = 852-4·(-250)·0
Δ = 7225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{7225}=85$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(85)-85}{2*-250}=\frac{-170}{-500}
=17/50
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(85)+85}{2*-250}=\frac{0}{-500}
=0
$