-x^2+x-1/16=0

Solution for -x^2+x-1/16=0 equation:

-x^2+x-1/16=0

We add all the numbers together, and all the variables

-1x^2+x-1/16=0

We multiply all the terms by the denominator


-1x^2*16+x*16-1=0

Wy multiply elements

-16x^2+16x-1=0

a = -16; b = 16; c = -1;
Δ = b2-4ac
Δ = 162-4·(-16)·(-1)
Δ = 192
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:

$\sqrt{\Delta}=\sqrt{192}=\sqrt{64*3}=\sqrt{64}*\sqrt{3}=8\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-8\sqrt{3}}{2*-16}=\frac{-16-8\sqrt{3}}{-32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+8\sqrt{3}}{2*-16}=\frac{-16+8\sqrt{3}}{-32}
$