7x^2=1/4

Solution for 7x^2=1/4 equation:

7x^2=1/4

We move all terms to the left:

7x^2-(1/4)=0

We add all the numbers together, and all the variables

7x^2-(+1/4)=0

We get rid of parentheses

7x^2-1/4=0

We multiply all the terms by the denominator


7x^2*4-1=0

Wy multiply elements

28x^2-1=0

a = 28; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·28·(-1)
Δ = 112
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:

$\sqrt{\Delta}=\sqrt{112}=\sqrt{16*7}=\sqrt{16}*\sqrt{7}=4\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{7}}{2*28}=\frac{0-4\sqrt{7}}{56}
=-\frac{4\sqrt{7}}{56}
=-\frac{\sqrt{7}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{7}}{2*28}=\frac{0+4\sqrt{7}}{56}
=\frac{4\sqrt{7}}{56}
=\frac{\sqrt{7}}{14}
$