-72+12=20z+8-1/3z

Solution for -72+12=20z+8-1/3z equation:

-72+12=20z+8-1/3z

We move all terms to the left:

-72+12-(20z+8-1/3z)=0


Domain of the equation: 3z)!=0

z!=0/1

z!=0

z∈R


We add all the numbers together, and all the variables

-(20z-1/3z+8)-72+12=0

We add all the numbers together, and all the variables

-(20z-1/3z+8)-60=0

We get rid of parentheses

-20z+1/3z-8-60=0

We multiply all the terms by the denominator


-20z*3z-8*3z-60*3z+1=0

Wy multiply elements

-60z^2-24z-180z+1=0

We add all the numbers together, and all the variables

-60z^2-204z+1=0

a = -60; b = -204; c = +1;
Δ = b2-4ac
Δ = -2042-4·(-60)·1
Δ = 41856
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{41856}=\sqrt{64*654}=\sqrt{64}*\sqrt{654}=8\sqrt{654}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-204)-8\sqrt{654}}{2*-60}=\frac{204-8\sqrt{654}}{-120}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-204)+8\sqrt{654}}{2*-60}=\frac{204+8\sqrt{654}}{-120}
$