-2x(x-3)+4x=-(x+1)

Solution for -2x(x-3)+4x=-(x+1) equation:

-2x(x-3)+4x=-(x+1)

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

-2x^2+4x+6x-(-(x+1))=0


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

-(x+1)

We get rid of parentheses

-x-1

We add all the numbers together, and all the variables

-1x-1

Back to the equation:

-(-1x-1)


We add all the numbers together, and all the variables

-2x^2+10x-(-1x-1)=0

We get rid of parentheses

-2x^2+10x+1x+1=0

We add all the numbers together, and all the variables

-2x^2+11x+1=0

a = -2; b = 11; c = +1;
Δ = b2-4ac
Δ = 112-4·(-2)·1
Δ = 129
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{-(11)-\sqrt{129}}{2*-2}=\frac{-11-\sqrt{129}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+\sqrt{129}}{2*-2}=\frac{-11+\sqrt{129}}{-4}
$