z^2/3=z/2+5/6 Quadratic formula

Question

(z^2)/3=z/3(z over 3)+5/6 (5 over 6).

Answer 1

if it is asking for your to find the value of z,

 

What I like to do is look at the denominator of each of the terms of the equation.

 

Your equation is  z²/3 = z/2 +(5/6).

 

But first I like to write all terms on the same side of the equation.

 

 

z²/3 - z/2 - 5/6 = 0

 

each of the number in the denominator of the equation are 2,3 and 6. 

Then I like to find the least common multiple of the three numbers:

 

2: 2,4,6 

3: 3,6

6: 6,12 

( above are the multiples of each of the three numbers, clearly the smallest common multiple is 6) 

 

so, What i like to do is multiply the whole equation by 6; 

 

6 ×( z²/3 - z/2 - (5/6) ) 

 

do the distributive property to get 

 

2z² - 3z - 5 = 0

 

A quadratic equation has the form:

 

az² + bz =c = 0

 

so here, a =2 , b = -3, and c = -5

 

To solve for z use the quadratic formula

 

 

z = (-b ±√( b² - 4ac) )/ 2a