X^2+210n=23

Solution for X^2+210n=23 equation:

X^2+210X=23

We move all terms to the left:

X^2+210X-(23)=0

a = 1; b = 210; c = -23;
Δ = b2-4ac
Δ = 2102-4·1·(-23)
Δ = 44192
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:

$\sqrt{\Delta}=\sqrt{44192}=\sqrt{16*2762}=\sqrt{16}*\sqrt{2762}=4\sqrt{2762}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(210)-4\sqrt{2762}}{2*1}=\frac{-210-4\sqrt{2762}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(210)+4\sqrt{2762}}{2*1}=\frac{-210+4\sqrt{2762}}{2}
$