-3(3x+4)+2x=8-9x(x-2)

Solution for -3(3x+4)+2x=8-9x(x-2) equation:

-3(3x+4)+2x=8-9x(x-2)

We move all terms to the left:

-3(3x+4)+2x-(8-9x(x-2))=0

We add all the numbers together, and all the variables

2x-3(3x+4)-(8-9x(x-2))=0

We multiply parentheses

2x-9x-(8-9x(x-2))-12=0


We calculate terms in parentheses: -(8-9x(x-2)), so:

8-9x(x-2)

determiningTheFunctionDomain
-9x(x-2)+8

We multiply parentheses

-9x^2+18x+8

Back to the equation:

-(-9x^2+18x+8)


We add all the numbers together, and all the variables

-(-9x^2+18x+8)-7x-12=0

We get rid of parentheses

9x^2-18x-7x-8-12=0

We add all the numbers together, and all the variables

9x^2-25x-20=0

a = 9; b = -25; c = -20;
Δ = b2-4ac
Δ = -252-4·9·(-20)
Δ = 1345
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-25)-\sqrt{1345}}{2*9}=\frac{25-\sqrt{1345}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+\sqrt{1345}}{2*9}=\frac{25+\sqrt{1345}}{18}
$