(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-1a-4)-6=0

We get rid of parentheses

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