x+8=2(0.5x+4)x

Solution for x+8=2(0.5x+4)x equation:

x+8=2(0.5x+4)x

We move all terms to the left:

x+8-(2(0.5x+4)x)=0


We calculate terms in parentheses: -(2(0.5x+4)x), so:

2(0.5x+4)x

We multiply parentheses

0x^2+8x

We add all the numbers together, and all the variables

x^2+8x

Back to the equation:

-(x^2+8x)


We get rid of parentheses

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

We add all the numbers together, and all the variables

-1x^2-7x+8=0

a = -1; b = -7; c = +8;
Δ = b2-4ac
Δ = -72-4·(-1)·8
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-9}{2*-1}=\frac{-2}{-2}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+9}{2*-1}=\frac{16}{-2}
=-8
$