(d+7)(d+4)=-2

Solution for (d+7)(d+4)=-2 equation:

(d+7)(d+4)=-2

We move all terms to the left:

(d+7)(d+4)-(-2)=0

We add all the numbers together, and all the variables

(d+7)(d+4)+2=0

We multiply parentheses ..

(+d^2+4d+7d+28)+2=0

We get rid of parentheses

d^2+4d+7d+28+2=0

We add all the numbers together, and all the variables

d^2+11d+30=0

a = 1; b = 11; c = +30;
Δ = b2-4ac
Δ = 112-4·1·30
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-1}{2*1}=\frac{-12}{2}
=-6
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+1}{2*1}=\frac{-10}{2}
=-5
$