(x+4)(x-4)=2x+5(x-4)

Solution for (x+4)(x-4)=2x+5(x-4) equation:

(x+4)(x-4)=2x+5(x-4)

We move all terms to the left:

(x+4)(x-4)-(2x+5(x-4))=0

We use the square of the difference formula

x^2-(2x+5(x-4))-16=0


We calculate terms in parentheses: -(2x+5(x-4)), so:

2x+5(x-4)

We multiply parentheses

2x+5x-20

We add all the numbers together, and all the variables

7x-20

Back to the equation:

-(7x-20)


We get rid of parentheses

x^2-7x+20-16=0

We add all the numbers together, and all the variables

x^2-7x+4=0

a = 1; b = -7; c = +4;
Δ = b2-4ac
Δ = -72-4·1·4
Δ = 33
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{-(-7)-\sqrt{33}}{2*1}=\frac{7-\sqrt{33}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{33}}{2*1}=\frac{7+\sqrt{33}}{2}
$