49x^2-14x+1=x

Solution for 49x^2-14x+1=x equation:

49x^2-14x+1=x

We move all terms to the left:

49x^2-14x+1-(x)=0

We add all the numbers together, and all the variables

49x^2-15x+1=0

a = 49; b = -15; c = +1;
Δ = b2-4ac
Δ = -152-4·49·1
Δ = 29
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{-(-15)-\sqrt{29}}{2*49}=\frac{15-\sqrt{29}}{98}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+\sqrt{29}}{2*49}=\frac{15+\sqrt{29}}{98}
$