3x-8=-x(x-2)

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

3x-8=-x(x-2)

We move all terms to the left:

3x-8-(-x(x-2))=0


We calculate terms in parentheses: -(-x(x-2)), so:

-x(x-2)

We multiply parentheses

-x^2+2x

We add all the numbers together, and all the variables

-1x^2+2x

Back to the equation:

-(-1x^2+2x)


We get rid of parentheses

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

We add all the numbers together, and all the variables

x^2+x-8=0

a = 1; b = 1; c = -8;
Δ = b2-4ac
Δ = 12-4·1·(-8)
Δ = 33
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{-(1)-\sqrt{33}}{2*1}=\frac{-1-\sqrt{33}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{33}}{2*1}=\frac{-1+\sqrt{33}}{2}
$