7500=d^2+520d

Solution for 7500=d^2+520d equation:

7500=d^2+520d

We move all terms to the left:

7500-(d^2+520d)=0

We get rid of parentheses

-d^2-520d+7500=0

We add all the numbers together, and all the variables

-1d^2-520d+7500=0

a = -1; b = -520; c = +7500;
Δ = b2-4ac
Δ = -5202-4·(-1)·7500
Δ = 300400
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:

$\sqrt{\Delta}=\sqrt{300400}=\sqrt{400*751}=\sqrt{400}*\sqrt{751}=20\sqrt{751}$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-520)-20\sqrt{751}}{2*-1}=\frac{520-20\sqrt{751}}{-2}
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-520)+20\sqrt{751}}{2*-1}=\frac{520+20\sqrt{751}}{-2}
$