(X-7)(x+3)=(x+6)

Solution for (X-7)(x+3)=(x+6) equation:

(X-7)(X+3)=(X+6)

We move all terms to the left:

(X-7)(X+3)-((X+6))=0

We multiply parentheses ..

(+X^2+3X-7X-21)-((X+6))=0


We calculate terms in parentheses: -((X+6)), so:

(X+6)

We get rid of parentheses

X+6

Back to the equation:

-(X+6)


We get rid of parentheses

X^2+3X-7X-X-21-6=0

We add all the numbers together, and all the variables

X^2-5X-27=0

a = 1; b = -5; c = -27;
Δ = b2-4ac
Δ = -52-4·1·(-27)
Δ = 133
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{-(-5)-\sqrt{133}}{2*1}=\frac{5-\sqrt{133}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{133}}{2*1}=\frac{5+\sqrt{133}}{2}
$