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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

3x-(x(x+8))+4=0


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

x(x+8)

We multiply parentheses

x^2+8x

Back to the equation:

-(x^2+8x)


We get rid of parentheses

-x^2+3x-8x+4=0

We add all the numbers together, and all the variables

-1x^2-5x+4=0

a = -1; b = -5; c = +4;
Δ = b2-4ac
Δ = -52-4·(-1)·4
Δ = 41
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{-(-5)-\sqrt{41}}{2*-1}=\frac{5-\sqrt{41}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{41}}{2*-1}=\frac{5+\sqrt{41}}{-2}
$