x^2=2187x+10935

Solution for x^2=2187x+10935 equation:

x^2=2187x+10935

We move all terms to the left:

x^2-(2187x+10935)=0

We get rid of parentheses

x^2-2187x-10935=0

a = 1; b = -2187; c = -10935;
Δ = b2-4ac
Δ = -21872-4·1·(-10935)
Δ = 4826709
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:

$\sqrt{\Delta}=\sqrt{4826709}=\sqrt{729*6621}=\sqrt{729}*\sqrt{6621}=27\sqrt{6621}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2187)-27\sqrt{6621}}{2*1}=\frac{2187-27\sqrt{6621}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2187)+27\sqrt{6621}}{2*1}=\frac{2187+27\sqrt{6621}}{2}
$