-2(1-3x)=22-3x(x-13)

Solution for -2(1-3x)=22-3x(x-13) equation:

-2(1-3x)=22-3x(x-13)

We move all terms to the left:

-2(1-3x)-(22-3x(x-13))=0

We add all the numbers together, and all the variables

-2(-3x+1)-(22-3x(x-13))=0

We multiply parentheses

6x-(22-3x(x-13))-2=0


We calculate terms in parentheses: -(22-3x(x-13)), so:

22-3x(x-13)

determiningTheFunctionDomain
-3x(x-13)+22

We multiply parentheses

-3x^2+39x+22

Back to the equation:

-(-3x^2+39x+22)


We get rid of parentheses

3x^2-39x+6x-22-2=0

We add all the numbers together, and all the variables

3x^2-33x-24=0

a = 3; b = -33; c = -24;
Δ = b2-4ac
Δ = -332-4·3·(-24)
Δ = 1377
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1377}=\sqrt{81*17}=\sqrt{81}*\sqrt{17}=9\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-33)-9\sqrt{17}}{2*3}=\frac{33-9\sqrt{17}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-33)+9\sqrt{17}}{2*3}=\frac{33+9\sqrt{17}}{6}
$