6*8=x(x+8)

Solution for 6*8=x(x+8) equation:

6*8=x(x+8)

We move all terms to the left:

6*8-(x(x+8))=0

We add all the numbers together, and all the variables

-(x(x+8))+48=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^2-8x+48=0

We add all the numbers together, and all the variables

-1x^2-8x+48=0

a = -1; b = -8; c = +48;
Δ = b2-4ac
Δ = -82-4·(-1)·48
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-16}{2*-1}=\frac{-8}{-2}
=+4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+16}{2*-1}=\frac{24}{-2}
=-12
$