4x^2-1/4=83/4

Solution for 4x^2-1/4=83/4 equation:

4x^2-1/4=83/4

We move all terms to the left:

4x^2-1/4-(83/4)=0

We add all the numbers together, and all the variables

4x^2-1/4-(+83/4)=0

We get rid of parentheses

4x^2-1/4-83/4=0

We multiply all the terms by the denominator


4x^2*4-1-83=0

We add all the numbers together, and all the variables

4x^2*4-84=0

Wy multiply elements

16x^2-84=0

a = 16; b = 0; c = -84;
Δ = b2-4ac
Δ = 02-4·16·(-84)
Δ = 5376
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:

$\sqrt{\Delta}=\sqrt{5376}=\sqrt{256*21}=\sqrt{256}*\sqrt{21}=16\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-16\sqrt{21}}{2*16}=\frac{0-16\sqrt{21}}{32}
=-\frac{16\sqrt{21}}{32}
=-\frac{\sqrt{21}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+16\sqrt{21}}{2*16}=\frac{0+16\sqrt{21}}{32}
=\frac{16\sqrt{21}}{32}
=\frac{\sqrt{21}}{2}
$