(r+6)(r-1)=-10

Solution for (r+6)(r-1)=-10 equation:

(r+6)(r-1)=-10

We move all terms to the left:

(r+6)(r-1)-(-10)=0

We add all the numbers together, and all the variables

(r+6)(r-1)+10=0

We multiply parentheses ..

(+r^2-1r+6r-6)+10=0

We get rid of parentheses

r^2-1r+6r-6+10=0

We add all the numbers together, and all the variables

r^2+5r+4=0

a = 1; b = 5; c = +4;
Δ = b2-4ac
Δ = 52-4·1·4
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-3}{2*1}=\frac{-8}{2}
=-4
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+3}{2*1}=\frac{-2}{2}
=-1
$