8-5x=2x(4+x)

Solution for 8-5x=2x(4+x) equation:

8-5x=2x(4+x)

We move all terms to the left:

8-5x-(2x(4+x))=0

We add all the numbers together, and all the variables

-5x-(2x(x+4))+8=0


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

2x(x+4)

We multiply parentheses

2x^2+8x

Back to the equation:

-(2x^2+8x)


We get rid of parentheses

-2x^2-5x-8x+8=0

We add all the numbers together, and all the variables

-2x^2-13x+8=0

a = -2; b = -13; c = +8;
Δ = b2-4ac
Δ = -132-4·(-2)·8
Δ = 233
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{-(-13)-\sqrt{233}}{2*-2}=\frac{13-\sqrt{233}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+\sqrt{233}}{2*-2}=\frac{13+\sqrt{233}}{-4}
$