8x^2=(x-2)(x)

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

8x^2=(x-2)(x)

We move all terms to the left:

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


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

(x-2)x

We multiply parentheses

x^2-2x

Back to the equation:

-(x^2-2x)


We get rid of parentheses

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

We add all the numbers together, and all the variables

7x^2+2x=0

a = 7; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·7·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2}{2*7}=\frac{-4}{14}
=-2/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2}{2*7}=\frac{0}{14}
=0
$