5(20-d)10d=130

Solution for 5(20-d)10d=130 equation:

5(20-d)10d=130

We move all terms to the left:

5(20-d)10d-(130)=0

We add all the numbers together, and all the variables

5(-1d+20)10d-130=0

We multiply parentheses

-50d^2+1000d-130=0

a = -50; b = 1000; c = -130;
Δ = b2-4ac
Δ = 10002-4·(-50)·(-130)
Δ = 974000
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:

$\sqrt{\Delta}=\sqrt{974000}=\sqrt{400*2435}=\sqrt{400}*\sqrt{2435}=20\sqrt{2435}$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1000)-20\sqrt{2435}}{2*-50}=\frac{-1000-20\sqrt{2435}}{-100}
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1000)+20\sqrt{2435}}{2*-50}=\frac{-1000+20\sqrt{2435}}{-100}
$