4819x-292999=839100+x*x

Solution for 4819x-292999=839100+x*x equation:

4819x-292999=839100+x*x

We move all terms to the left:

4819x-292999-(839100+x*x)=0

We add all the numbers together, and all the variables

4819x-(x*x+839100)-292999=0

We get rid of parentheses

4819x-x*x-839100-292999=0

We add all the numbers together, and all the variables

4819x-x*x-1132099=0

Wy multiply elements

-1x^2+4819x-1132099=0

a = -1; b = 4819; c = -1132099;
Δ = b2-4ac
Δ = 48192-4·(-1)·(-1132099)
Δ = 18694365
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4819)-\sqrt{18694365}}{2*-1}=\frac{-4819-\sqrt{18694365}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4819)+\sqrt{18694365}}{2*-1}=\frac{-4819+\sqrt{18694365}}{-2}
$