1500=4x^2+380x+8400

Solution for 1500=4x^2+380x+8400 equation:

1500=4x^2+380x+8400

We move all terms to the left:

1500-(4x^2+380x+8400)=0

We get rid of parentheses

-4x^2-380x-8400+1500=0

We add all the numbers together, and all the variables

-4x^2-380x-6900=0

a = -4; b = -380; c = -6900;
Δ = b2-4ac
Δ = -3802-4·(-4)·(-6900)
Δ = 34000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{34000}=\sqrt{400*85}=\sqrt{400}*\sqrt{85}=20\sqrt{85}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-380)-20\sqrt{85}}{2*-4}=\frac{380-20\sqrt{85}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-380)+20\sqrt{85}}{2*-4}=\frac{380+20\sqrt{85}}{-8}
$