2x+8=4(-3x+x^2)

Solution for 2x+8=4(-3x+x^2) equation:

2x+8=4(-3x+x^2)

We move all terms to the left:

2x+8-(4(-3x+x^2))=0


We calculate terms in parentheses: -(4(-3x+x^2)), so:

4(-3x+x^2)

We multiply parentheses

4x^2-12x

Back to the equation:

-(4x^2-12x)


We add all the numbers together, and all the variables

2x-(4x^2-12x)+8=0

We get rid of parentheses

-4x^2+2x+12x+8=0

We add all the numbers together, and all the variables

-4x^2+14x+8=0

a = -4; b = 14; c = +8;
Δ = b2-4ac
Δ = 142-4·(-4)·8
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-18}{2*-4}=\frac{-32}{-8}
=+4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+18}{2*-4}=\frac{4}{-8}
=-1/2
$