x^2+900x-12*10^3=4

Solution for x^2+900x-12*10^3=4 equation:

x^2+900x-12*10^3=4

We move all terms to the left:

x^2+900x-12*10^3-(4)=0

determiningTheFunctionDomain
x^2+900x-4-12*10^3=0

We add all the numbers together, and all the variables

x^2+900x-12004=0

a = 1; b = 900; c = -12004;
Δ = b2-4ac
Δ = 9002-4·1·(-12004)
Δ = 858016
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:

$\sqrt{\Delta}=\sqrt{858016}=\sqrt{16*53626}=\sqrt{16}*\sqrt{53626}=4\sqrt{53626}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(900)-4\sqrt{53626}}{2*1}=\frac{-900-4\sqrt{53626}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(900)+4\sqrt{53626}}{2*1}=\frac{-900+4\sqrt{53626}}{2}
$