x*x=45775

Solution for x*x=45775 equation:

x*x=45775

We move all terms to the left:

x*x-(45775)=0

Wy multiply elements

x^2-45775=0

a = 1; b = 0; c = -45775;
Δ = b2-4ac
Δ = 02-4·1·(-45775)
Δ = 183100
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:

$\sqrt{\Delta}=\sqrt{183100}=\sqrt{100*1831}=\sqrt{100}*\sqrt{1831}=10\sqrt{1831}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{1831}}{2*1}=\frac{0-10\sqrt{1831}}{2}
=-\frac{10\sqrt{1831}}{2}
=-5\sqrt{1831}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{1831}}{2*1}=\frac{0+10\sqrt{1831}}{2}
=\frac{10\sqrt{1831}}{2}
=5\sqrt{1831}
$