4/15z+5/6z+1/2=8/5

Solution for 4/15z+5/6z+1/2=8/5 equation:

4/15z+5/6z+1/2=8/5

We move all terms to the left:

4/15z+5/6z+1/2-(8/5)=0


Domain of the equation: 15z!=0

z!=0/15

z!=0

z∈R



Domain of the equation: 6z!=0

z!=0/6

z!=0

z∈R


We add all the numbers together, and all the variables

4/15z+5/6z+1/2-(+8/5)=0

We get rid of parentheses

4/15z+5/6z+1/2-8/5=0

We calculate fractions


(-8640z^2)/1800z^2+2700z^2/1800z^2+480z/1800z^2+1500z/1800z^2=0

We multiply all the terms by the denominator


(-8640z^2)+2700z^2+480z+1500z=0

We add all the numbers together, and all the variables

2700z^2+(-8640z^2)+1980z=0

We get rid of parentheses

2700z^2-8640z^2+1980z=0

We add all the numbers together, and all the variables

-5940z^2+1980z=0

a = -5940; b = 1980; c = 0;
Δ = b2-4ac
Δ = 19802-4·(-5940)·0
Δ = 3920400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3920400}=1980$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1980)-1980}{2*-5940}=\frac{-3960}{-11880}
=1/3
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1980)+1980}{2*-5940}=\frac{0}{-11880}
=0
$