(x+6)(x-6)=13(x+8)

Solution for (x+6)(x-6)=13(x+8) equation:

(x+6)(x-6)=13(x+8)

We move all terms to the left:

(x+6)(x-6)-(13(x+8))=0

We use the square of the difference formula

x^2-(13(x+8))-36=0


We calculate terms in parentheses: -(13(x+8)), so:

13(x+8)

We multiply parentheses

13x+104

Back to the equation:

-(13x+104)


We get rid of parentheses

x^2-13x-104-36=0

We add all the numbers together, and all the variables

x^2-13x-140=0

a = 1; b = -13; c = -140;
Δ = b2-4ac
Δ = -132-4·1·(-140)
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-27}{2*1}=\frac{-14}{2}
=-7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+27}{2*1}=\frac{40}{2}
=20
$