105=(x)(x+8)

Solution for 105=(x)(x+8) equation:

105=(x)(x+8)

We move all terms to the left:

105-((x)(x+8))=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+105=0

We add all the numbers together, and all the variables

-1x^2-8x+105=0

a = -1; b = -8; c = +105;
Δ = b2-4ac
Δ = -82-4·(-1)·105
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-22}{2*-1}=\frac{-14}{-2}
=+7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+22}{2*-1}=\frac{30}{-2}
=-15
$