4x^2+x-(1/16)=0

Solution for 4x^2+x-(1/16)=0 equation:

4x^2+x-(1/16)=0

We add all the numbers together, and all the variables

4x^2+x-(+1/16)=0

We get rid of parentheses

4x^2+x-1/16=0

We multiply all the terms by the denominator


4x^2*16+x*16-1=0

Wy multiply elements

64x^2+16x-1=0

a = 64; b = 16; c = -1;
Δ = b2-4ac
Δ = 162-4·64·(-1)
Δ = 512
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:

$\sqrt{\Delta}=\sqrt{512}=\sqrt{256*2}=\sqrt{256}*\sqrt{2}=16\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-16\sqrt{2}}{2*64}=\frac{-16-16\sqrt{2}}{128}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+16\sqrt{2}}{2*64}=\frac{-16+16\sqrt{2}}{128}
$