-2x(x-2)+4x=-3(x+4)+13

Solution for -2x(x-2)+4x=-3(x+4)+13 equation:

-2x(x-2)+4x=-3(x+4)+13

We move all terms to the left:

-2x(x-2)+4x-(-3(x+4)+13)=0

We add all the numbers together, and all the variables

4x-2x(x-2)-(-3(x+4)+13)=0

We multiply parentheses

-2x^2+4x+4x-(-3(x+4)+13)=0


We calculate terms in parentheses: -(-3(x+4)+13), so:

-3(x+4)+13

We multiply parentheses

-3x-12+13

We add all the numbers together, and all the variables

-3x+1

Back to the equation:

-(-3x+1)


We add all the numbers together, and all the variables

-2x^2+8x-(-3x+1)=0

We get rid of parentheses

-2x^2+8x+3x-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 = 113
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{113}}{2*-2}=\frac{-11-\sqrt{113}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+\sqrt{113}}{2*-2}=\frac{-11+\sqrt{113}}{-4}
$