2x(x-8)=(x+1)(x+6)

Solution for 2x(x-8)=(x+1)(x+6) equation:

2x(x-8)=(x+1)(x+6)

We move all terms to the left:

2x(x-8)-((x+1)(x+6))=0

We multiply parentheses

2x^2-16x-((x+1)(x+6))=0

We multiply parentheses ..

2x^2-((+x^2+6x+x+6))-16x=0


We calculate terms in parentheses: -((+x^2+6x+x+6)), so:

(+x^2+6x+x+6)

We get rid of parentheses

x^2+6x+x+6

We add all the numbers together, and all the variables

x^2+7x+6

Back to the equation:

-(x^2+7x+6)


We add all the numbers together, and all the variables

2x^2-16x-(x^2+7x+6)=0

We get rid of parentheses

2x^2-x^2-16x-7x-6=0

We add all the numbers together, and all the variables

x^2-23x-6=0

a = 1; b = -23; c = -6;
Δ = b2-4ac
Δ = -232-4·1·(-6)
Δ = 553
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{-(-23)-\sqrt{553}}{2*1}=\frac{23-\sqrt{553}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+\sqrt{553}}{2*1}=\frac{23+\sqrt{553}}{2}
$