4x2-x=4096

Solution for 4x2-x=4096 equation:

4x^2-x=4096

We move all terms to the left:

4x^2-x-(4096)=0

We add all the numbers together, and all the variables

4x^2-1x-4096=0

a = 4; b = -1; c = -4096;
Δ = b2-4ac
Δ = -12-4·4·(-4096)
Δ = 65537
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{65537}}{2*4}=\frac{1-\sqrt{65537}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{65537}}{2*4}=\frac{1+\sqrt{65537}}{8}
$