(8d+4)(6d+8)=180

Solution for (8d+4)(6d+8)=180 equation:

(8d+4)(6d+8)=180

We move all terms to the left:

(8d+4)(6d+8)-(180)=0

We multiply parentheses ..

(+48d^2+64d+24d+32)-180=0

We get rid of parentheses

48d^2+64d+24d+32-180=0

We add all the numbers together, and all the variables

48d^2+88d-148=0

a = 48; b = 88; c = -148;
Δ = b2-4ac
Δ = 882-4·48·(-148)
Δ = 36160
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{36160}=\sqrt{64*565}=\sqrt{64}*\sqrt{565}=8\sqrt{565}$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(88)-8\sqrt{565}}{2*48}=\frac{-88-8\sqrt{565}}{96}
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(88)+8\sqrt{565}}{2*48}=\frac{-88+8\sqrt{565}}{96}
$