(m+8)(m-9)=(m+1)

Solution for (m+8)(m-9)=(m+1) equation:

(m+8)(m-9)=(m+1)

We move all terms to the left:

(m+8)(m-9)-((m+1))=0

We multiply parentheses ..

(+m^2-9m+8m-72)-((m+1))=0


We calculate terms in parentheses: -((m+1)), so:

(m+1)

We get rid of parentheses

m+1

Back to the equation:

-(m+1)


We get rid of parentheses

m^2-9m+8m-m-72-1=0

We add all the numbers together, and all the variables

m^2-2m-73=0

a = 1; b = -2; c = -73;
Δ = b2-4ac
Δ = -22-4·1·(-73)
Δ = 296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{296}=\sqrt{4*74}=\sqrt{4}*\sqrt{74}=2\sqrt{74}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{74}}{2*1}=\frac{2-2\sqrt{74}}{2}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{74}}{2*1}=\frac{2+2\sqrt{74}}{2}
$