250x^2-245x+49=x

Solution for 250x^2-245x+49=x equation:

250x^2-245x+49=x

We move all terms to the left:

250x^2-245x+49-(x)=0

We add all the numbers together, and all the variables

250x^2-246x+49=0

a = 250; b = -246; c = +49;
Δ = b2-4ac
Δ = -2462-4·250·49
Δ = 11516
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:

$\sqrt{\Delta}=\sqrt{11516}=\sqrt{4*2879}=\sqrt{4}*\sqrt{2879}=2\sqrt{2879}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-246)-2\sqrt{2879}}{2*250}=\frac{246-2\sqrt{2879}}{500}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-246)+2\sqrt{2879}}{2*250}=\frac{246+2\sqrt{2879}}{500}
$