x^2=1540

Solution for x^2=1540 equation:

x^2=1540

We move all terms to the left:

x^2-(1540)=0

a = 1; b = 0; c = -1540;
Δ = b2-4ac
Δ = 02-4·1·(-1540)
Δ = 6160
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:

$\sqrt{\Delta}=\sqrt{6160}=\sqrt{16*385}=\sqrt{16}*\sqrt{385}=4\sqrt{385}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{385}}{2*1}=\frac{0-4\sqrt{385}}{2}
=-\frac{4\sqrt{385}}{2}
=-2\sqrt{385}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{385}}{2*1}=\frac{0+4\sqrt{385}}{2}
=\frac{4\sqrt{385}}{2}
=2\sqrt{385}
$