(m+5)(m-1)=7

Solution for (m+5)(m-1)=7 equation:

(m+5)(m-1)=7

We move all terms to the left:

(m+5)(m-1)-(7)=0

We multiply parentheses ..

(+m^2-1m+5m-5)-7=0

We get rid of parentheses

m^2-1m+5m-5-7=0

We add all the numbers together, and all the variables

m^2+4m-12=0

a = 1; b = 4; c = -12;
Δ = b2-4ac
Δ = 42-4·1·(-12)
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-8}{2*1}=\frac{-12}{2}
=-6
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+8}{2*1}=\frac{4}{2}
=2
$