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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

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


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

22-3(x-13)

determiningTheFunctionDomain
-3(x-13)+22

We multiply parentheses

-3x+39+22

We add all the numbers together, and all the variables

-3x+61

Back to the equation:

-(-3x+61)


We get rid of parentheses

6x^2-2x+3x-61=0

We add all the numbers together, and all the variables

6x^2+x-61=0

a = 6; b = 1; c = -61;
Δ = b2-4ac
Δ = 12-4·6·(-61)
Δ = 1465
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{-(1)-\sqrt{1465}}{2*6}=\frac{-1-\sqrt{1465}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{1465}}{2*6}=\frac{-1+\sqrt{1465}}{12}
$