3(x-1)-2(2x+3)=2x(3-x)+2x-5x

Solution for 3(x-1)-2(2x+3)=2x(3-x)+2x-5x equation:

3(x-1)-2(2x+3)=2x(3-x)+2x-5x

We move all terms to the left:

3(x-1)-2(2x+3)-(2x(3-x)+2x-5x)=0

We add all the numbers together, and all the variables

3(x-1)-2(2x+3)-(2x(-1x+3)+2x-5x)=0

We multiply parentheses

3x-4x-(2x(-1x+3)+2x-5x)-3-6=0


We calculate terms in parentheses: -(2x(-1x+3)+2x-5x), so:

2x(-1x+3)+2x-5x

We add all the numbers together, and all the variables

-3x+2x(-1x+3)

We multiply parentheses

-2x^2-3x+6x

We add all the numbers together, and all the variables

-2x^2+3x

Back to the equation:

-(-2x^2+3x)


We add all the numbers together, and all the variables

-(-2x^2+3x)-1x-9=0

We get rid of parentheses

2x^2-3x-1x-9=0

We add all the numbers together, and all the variables

2x^2-4x-9=0

a = 2; b = -4; c = -9;
Δ = b2-4ac
Δ = -42-4·2·(-9)
Δ = 88
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:

$\sqrt{\Delta}=\sqrt{88}=\sqrt{4*22}=\sqrt{4}*\sqrt{22}=2\sqrt{22}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{22}}{2*2}=\frac{4-2\sqrt{22}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{22}}{2*2}=\frac{4+2\sqrt{22}}{4}
$