(5d-7)(6d+8)=A

Solution for (5d-7)(6d+8)=A equation:

(5d-7)(6d+8)=

We move all terms to the left:

(5d-7)(6d+8)-()=0

We add all the numbers together, and all the variables

(5d-7)(6d+8)=0

We multiply parentheses ..

(+30d^2+40d-42d-56)=0

We get rid of parentheses

30d^2+40d-42d-56=0

We add all the numbers together, and all the variables

30d^2-2d-56=0

a = 30; b = -2; c = -56;
Δ = b2-4ac
Δ = -22-4·30·(-56)
Δ = 6724
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6724}=82$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-82}{2*30}=\frac{-80}{60}
=-1+1/3
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+82}{2*30}=\frac{84}{60}
=1+2/5
$