x^2=14/16

Solution for x^2=14/16 equation:

x^2=14/16

We move all terms to the left:

x^2-(14/16)=0

We add all the numbers together, and all the variables

x^2-(+14/16)=0

We get rid of parentheses

x^2-14/16=0

We multiply all the terms by the denominator


x^2*16-14=0

Wy multiply elements

16x^2-14=0

a = 16; b = 0; c = -14;
Δ = b2-4ac
Δ = 02-4·16·(-14)
Δ = 896
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:

$\sqrt{\Delta}=\sqrt{896}=\sqrt{64*14}=\sqrt{64}*\sqrt{14}=8\sqrt{14}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{14}}{2*16}=\frac{0-8\sqrt{14}}{32}
=-\frac{8\sqrt{14}}{32}
=-\frac{\sqrt{14}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{14}}{2*16}=\frac{0+8\sqrt{14}}{32}
=\frac{8\sqrt{14}}{32}
=\frac{\sqrt{14}}{4}
$