x2+100=52x

Solution for x2+100=52x equation:

x2+100=52x

We move all terms to the left:

x2+100-(52x)=0

We add all the numbers together, and all the variables

x^2-52x+100=0

a = 1; b = -52; c = +100;
Δ = b2-4ac
Δ = -522-4·1·100
Δ = 2304
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2304}=48$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-52)-48}{2*1}=\frac{4}{2}
=2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-52)+48}{2*1}=\frac{100}{2}
=50
$