(x+5)(x-5)=11(x+7)

Solution for (x+5)(x-5)=11(x+7) equation:

(x+5)(x-5)=11(x+7)

We move all terms to the left:

(x+5)(x-5)-(11(x+7))=0

We use the square of the difference formula

x^2-(11(x+7))-25=0


We calculate terms in parentheses: -(11(x+7)), so:

11(x+7)

We multiply parentheses

11x+77

Back to the equation:

-(11x+77)


We get rid of parentheses

x^2-11x-77-25=0

We add all the numbers together, and all the variables

x^2-11x-102=0

a = 1; b = -11; c = -102;
Δ = b2-4ac
Δ = -112-4·1·(-102)
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-23}{2*1}=\frac{-12}{2}
=-6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+23}{2*1}=\frac{34}{2}
=17
$