625+4225=x^2

Solution for 625+4225=x^2 equation:

625+4225=x^2

We move all terms to the left:

625+4225-(x^2)=0

We add all the numbers together, and all the variables

-1x^2+4850=0

a = -1; b = 0; c = +4850;
Δ = b2-4ac
Δ = 02-4·(-1)·4850
Δ = 19400
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:

$\sqrt{\Delta}=\sqrt{19400}=\sqrt{100*194}=\sqrt{100}*\sqrt{194}=10\sqrt{194}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{194}}{2*-1}=\frac{0-10\sqrt{194}}{-2}
=-\frac{10\sqrt{194}}{-2}
=-\frac{5\sqrt{194}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{194}}{2*-1}=\frac{0+10\sqrt{194}}{-2}
=\frac{10\sqrt{194}}{-2}
=\frac{5\sqrt{194}}{-1}
$