x2=1519

Solution for x2=1519 equation:

x2=1519

We move all terms to the left:

x2-(1519)=0

We add all the numbers together, and all the variables

x^2-1519=0

a = 1; b = 0; c = -1519;
Δ = b2-4ac
Δ = 02-4·1·(-1519)
Δ = 6076
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:

$\sqrt{\Delta}=\sqrt{6076}=\sqrt{196*31}=\sqrt{196}*\sqrt{31}=14\sqrt{31}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-14\sqrt{31}}{2*1}=\frac{0-14\sqrt{31}}{2}
=-\frac{14\sqrt{31}}{2}
=-7\sqrt{31}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+14\sqrt{31}}{2*1}=\frac{0+14\sqrt{31}}{2}
=\frac{14\sqrt{31}}{2}
=7\sqrt{31}
$