1=8x2-1/4

Solution for 1=8x2-1/4 equation:

1=8x^2-1/4

We move all terms to the left:

1-(8x^2-1/4)=0

We get rid of parentheses

-8x^2+1+1/4=0

We multiply all the terms by the denominator


-8x^2*4+1+1*4=0

We add all the numbers together, and all the variables

-8x^2*4+5=0

Wy multiply elements

-32x^2+5=0

a = -32; b = 0; c = +5;
Δ = b2-4ac
Δ = 02-4·(-32)·5
Δ = 640
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:

$\sqrt{\Delta}=\sqrt{640}=\sqrt{64*10}=\sqrt{64}*\sqrt{10}=8\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{10}}{2*-32}=\frac{0-8\sqrt{10}}{-64}
=-\frac{8\sqrt{10}}{-64}
=-\frac{\sqrt{10}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{10}}{2*-32}=\frac{0+8\sqrt{10}}{-64}
=\frac{8\sqrt{10}}{-64}
=\frac{\sqrt{10}}{-8}
$