625+x^2=1089

Solution for 625+x^2=1089 equation:

625+x^2=1089

We move all terms to the left:

625+x^2-(1089)=0

We add all the numbers together, and all the variables

x^2-464=0

a = 1; b = 0; c = -464;
Δ = b2-4ac
Δ = 02-4·1·(-464)
Δ = 1856
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:

$\sqrt{\Delta}=\sqrt{1856}=\sqrt{64*29}=\sqrt{64}*\sqrt{29}=8\sqrt{29}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{29}}{2*1}=\frac{0-8\sqrt{29}}{2}
=-\frac{8\sqrt{29}}{2}
=-4\sqrt{29}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{29}}{2*1}=\frac{0+8\sqrt{29}}{2}
=\frac{8\sqrt{29}}{2}
=4\sqrt{29}
$