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

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

a = 2; b = 0; c = -14;
Δ = b2-4ac
Δ = 02-4·2·(-14)
Δ = 112
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:

$\sqrt{\Delta}=\sqrt{112}=\sqrt{16*7}=\sqrt{16}*\sqrt{7}=4\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{7}}{2*2}=\frac{0-4\sqrt{7}}{4}
=-\frac{4\sqrt{7}}{4}
=-\sqrt{7}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{7}}{2*2}=\frac{0+4\sqrt{7}}{4}
=\frac{4\sqrt{7}}{4}
=\sqrt{7}
$