x(x+8)=8(8+x+12)

Solution for x(x+8)=8(8+x+12) equation:

x(x+8)=8(8+x+12)

We move all terms to the left:

x(x+8)-(8(8+x+12))=0

We add all the numbers together, and all the variables

x(x+8)-(8(x+20))=0

We multiply parentheses

x^2+8x-(8(x+20))=0


We calculate terms in parentheses: -(8(x+20)), so:

8(x+20)

We multiply parentheses

8x+160

Back to the equation:

-(8x+160)


We get rid of parentheses

x^2+8x-8x-160=0

We add all the numbers together, and all the variables

x^2-160=0

a = 1; b = 0; c = -160;
Δ = b2-4ac
Δ = 02-4·1·(-160)
Δ = 640
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{640}=\sqrt{64*10}=\sqrt{64}*\sqrt{10}=8\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{10}}{2*1}=\frac{0-8\sqrt{10}}{2}
=-\frac{8\sqrt{10}}{2}
=-4\sqrt{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{10}}{2*1}=\frac{0+8\sqrt{10}}{2}
=\frac{8\sqrt{10}}{2}
=4\sqrt{10}
$