20(7-d)11d=113

Solution for 20(7-d)11d=113 equation:

20(7-d)11d=113

We move all terms to the left:

20(7-d)11d-(113)=0

We add all the numbers together, and all the variables

20(-1d+7)11d-113=0

We multiply parentheses

-220d^2+1540d-113=0

a = -220; b = 1540; c = -113;
Δ = b2-4ac
Δ = 15402-4·(-220)·(-113)
Δ = 2272160
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:

$\sqrt{\Delta}=\sqrt{2272160}=\sqrt{16*142010}=\sqrt{16}*\sqrt{142010}=4\sqrt{142010}$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1540)-4\sqrt{142010}}{2*-220}=\frac{-1540-4\sqrt{142010}}{-440}
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1540)+4\sqrt{142010}}{2*-220}=\frac{-1540+4\sqrt{142010}}{-440}
$