0.62532-3.6477x+5.211x^2=x

Solution for 0.62532-3.6477x+5.211x^2=x equation:

0.62532-3.6477x+5.211x^2=x

We move all terms to the left:

0.62532-3.6477x+5.211x^2-(x)=0

We add all the numbers together, and all the variables

5.211x^2-4.6477x+0.62532=0

a = 5.211; b = -4.6477; c = +0.62532;
Δ = b2-4ac
Δ = -4.64772-4·5.211·0.62532
Δ = 8.56694521
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4.6477)-\sqrt{8.56694521}}{2*5.211}=\frac{4.6477-\sqrt{8.56694521}}{10.422}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4.6477)+\sqrt{8.56694521}}{2*5.211}=\frac{4.6477+\sqrt{8.56694521}}{10.422}
$