4/5z-5=-2+5/6z

Solution for 4/5z-5=-2+5/6z equation:

4/5z-5=-2+5/6z

We move all terms to the left:

4/5z-5-(-2+5/6z)=0


Domain of the equation: 5z!=0

z!=0/5

z!=0

z∈R



Domain of the equation: 6z)!=0

z!=0/1

z!=0

z∈R


We add all the numbers together, and all the variables

4/5z-(5/6z-2)-5=0

We get rid of parentheses

4/5z-5/6z+2-5=0

We calculate fractions


24z/30z^2+(-25z)/30z^2+2-5=0

We add all the numbers together, and all the variables

24z/30z^2+(-25z)/30z^2-3=0

We multiply all the terms by the denominator


24z+(-25z)-3*30z^2=0

Wy multiply elements

-90z^2+24z+(-25z)=0

We get rid of parentheses

-90z^2+24z-25z=0

We add all the numbers together, and all the variables

-90z^2-1z=0

a = -90; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·(-90)·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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