3(2x-1)-11=-2x(3-x)

Solution for 3(2x-1)-11=-2x(3-x) equation:

3(2x-1)-11=-2x(3-x)

We move all terms to the left:

3(2x-1)-11-(-2x(3-x))=0

We add all the numbers together, and all the variables

3(2x-1)-(-2x(-1x+3))-11=0

We multiply parentheses

6x-(-2x(-1x+3))-3-11=0


We calculate terms in parentheses: -(-2x(-1x+3)), so:

-2x(-1x+3)

We multiply parentheses

2x^2-6x

Back to the equation:

-(2x^2-6x)


We add all the numbers together, and all the variables

6x-(2x^2-6x)-14=0

We get rid of parentheses

-2x^2+6x+6x-14=0

We add all the numbers together, and all the variables

-2x^2+12x-14=0

a = -2; b = 12; c = -14;
Δ = b2-4ac
Δ = 122-4·(-2)·(-14)
Δ = 32
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:

$\sqrt{\Delta}=\sqrt{32}=\sqrt{16*2}=\sqrt{16}*\sqrt{2}=4\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-4\sqrt{2}}{2*-2}=\frac{-12-4\sqrt{2}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+4\sqrt{2}}{2*-2}=\frac{-12+4\sqrt{2}}{-4}
$