(x+3)(x-3)=5(x-3)

Solution for (x+3)(x-3)=5(x-3) equation:

(x+3)(x-3)=5(x-3)

We move all terms to the left:

(x+3)(x-3)-(5(x-3))=0

We use the square of the difference formula

x^2-(5(x-3))-9=0


We calculate terms in parentheses: -(5(x-3)), so:

5(x-3)

We multiply parentheses

5x-15

Back to the equation:

-(5x-15)


We get rid of parentheses

x^2-5x+15-9=0

We add all the numbers together, and all the variables

x^2-5x+6=0

a = 1; b = -5; c = +6;
Δ = b2-4ac
Δ = -52-4·1·6
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-1}{2*1}=\frac{4}{2}
=2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+1}{2*1}=\frac{6}{2}
=3
$