6z-36=4(z-9)6z-36-2z=4(z-9)6z-36-2z=6(z-9)6z-9-2z=4(z-9)

Solution for 6z-36=4(z-9)6z-36-2z=4(z-9)6z-36-2z=6(z-9)6z-9-2z=4(z-9) equation:

6z-36=4(z-9)6z-36-2z=4(z-9)6z-36-2z=6(z-9)6z-9-2z=4(z-9)

We move all terms to the left:

6z-36-(4(z-9)6z-36-2z)=0


We calculate terms in parentheses: -(4(z-9)6z-36-2z), so:

4(z-9)6z-36-2z

determiningTheFunctionDomain
4(z-9)6z-2z-36

We add all the numbers together, and all the variables

-2z+4(z-9)6z-36

We multiply parentheses

24z^2-2z-216z-36

We add all the numbers together, and all the variables

24z^2-218z-36

Back to the equation:

-(24z^2-218z-36)


We get rid of parentheses

-24z^2+6z+218z+36-36=0

We add all the numbers together, and all the variables

-24z^2+224z=0

a = -24; b = 224; c = 0;
Δ = b2-4ac
Δ = 2242-4·(-24)·0
Δ = 50176
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{50176}=224$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(224)-224}{2*-24}=\frac{-448}{-48}
=9+1/3
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(224)+224}{2*-24}=\frac{0}{-48}
=0
$