10x^2+x+1=6561

Solution for 10x^2+x+1=6561 equation:

10x^2+x+1=6561

We move all terms to the left:

10x^2+x+1-(6561)=0

We add all the numbers together, and all the variables

10x^2+x-6560=0

a = 10; b = 1; c = -6560;
Δ = b2-4ac
Δ = 12-4·10·(-6560)
Δ = 262401
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{-(1)-\sqrt{262401}}{2*10}=\frac{-1-\sqrt{262401}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{262401}}{2*10}=\frac{-1+\sqrt{262401}}{20}
$