x-9(4+2x)+33=4-6(3x-1)x=

Solution for x-9(4+2x)+33=4-6(3x-1)x= equation:

x-9(4+2x)+33=4-6(3x-1)x=

We move all terms to the left:

x-9(4+2x)+33-(4-6(3x-1)x)=0

We add all the numbers together, and all the variables

x-9(2x+4)-(4-6(3x-1)x)+33=0

We multiply parentheses

x-18x-(4-6(3x-1)x)-36+33=0


We calculate terms in parentheses: -(4-6(3x-1)x), so:

4-6(3x-1)x

determiningTheFunctionDomain
-6(3x-1)x+4

We multiply parentheses

-18x^2+6x+4

Back to the equation:

-(-18x^2+6x+4)


We add all the numbers together, and all the variables

-(-18x^2+6x+4)-17x-3=0

We get rid of parentheses

18x^2-6x-17x-4-3=0

We add all the numbers together, and all the variables

18x^2-23x-7=0

a = 18; b = -23; c = -7;
Δ = b2-4ac
Δ = -232-4·18·(-7)
Δ = 1033
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{-(-23)-\sqrt{1033}}{2*18}=\frac{23-\sqrt{1033}}{36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+\sqrt{1033}}{2*18}=\frac{23+\sqrt{1033}}{36}
$