X2-100x+2500=1250

Solution for X2-100x+2500=1250 equation:

X2-100X+2500=1250

We move all terms to the left:

X2-100X+2500-(1250)=0

We add all the numbers together, and all the variables

X^2-100X+1250=0

a = 1; b = -100; c = +1250;
Δ = b2-4ac
Δ = -1002-4·1·1250
Δ = 5000
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:

$\sqrt{\Delta}=\sqrt{5000}=\sqrt{2500*2}=\sqrt{2500}*\sqrt{2}=50\sqrt{2}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-100)-50\sqrt{2}}{2*1}=\frac{100-50\sqrt{2}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-100)+50\sqrt{2}}{2*1}=\frac{100+50\sqrt{2}}{2}
$