5x=2x(8-x)

Solution for 5x=2x(8-x) equation:

5x=2x(8-x)

We move all terms to the left:

5x-(2x(8-x))=0

We add all the numbers together, and all the variables

5x-(2x(-1x+8))=0


We calculate terms in parentheses: -(2x(-1x+8)), so:

2x(-1x+8)

We multiply parentheses

-2x^2+16x

Back to the equation:

-(-2x^2+16x)


We get rid of parentheses

2x^2-16x+5x=0

We add all the numbers together, and all the variables

2x^2-11x=0

a = 2; b = -11; c = 0;
Δ = b2-4ac
Δ = -112-4·2·0
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-11}{2*2}=\frac{0}{4}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+11}{2*2}=\frac{22}{4}
=5+1/2
$