(a+1)(a-4)=6

Solution for (a+1)(a-4)=6 equation:

(a+1)(a-4)=6

We move all terms to the left:

(a+1)(a-4)-(6)=0

We multiply parentheses ..

(+a^2-4a+a-4)-6=0

We get rid of parentheses

a^2-4a+a-4-6=0

We add all the numbers together, and all the variables

a^2-3a-10=0

a = 1; b = -3; c = -10;
Δ = b2-4ac
Δ = -32-4·1·(-10)
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-7}{2*1}=\frac{-4}{2}
=-2
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+7}{2*1}=\frac{10}{2}
=5
$