x2+1x=51x

Solution for x2+1x=51x equation:

x2+1x=51x

We move all terms to the left:

x2+1x-(51x)=0

We add all the numbers together, and all the variables

x^2-50x=0

a = 1; b = -50; c = 0;
Δ = b2-4ac
Δ = -502-4·1·0
Δ = 2500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2500}=50$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-50}{2*1}=\frac{0}{2}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+50}{2*1}=\frac{100}{2}
=50
$