x^2=23/16

Solution for x^2=23/16 equation:

x^2=23/16

We move all terms to the left:

x^2-(23/16)=0

We add all the numbers together, and all the variables

x^2-(+23/16)=0

We get rid of parentheses

x^2-23/16=0

We multiply all the terms by the denominator


x^2*16-23=0

Wy multiply elements

16x^2-23=0

a = 16; b = 0; c = -23;
Δ = b2-4ac
Δ = 02-4·16·(-23)
Δ = 1472
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:

$\sqrt{\Delta}=\sqrt{1472}=\sqrt{64*23}=\sqrt{64}*\sqrt{23}=8\sqrt{23}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{23}}{2*16}=\frac{0-8\sqrt{23}}{32}
=-\frac{8\sqrt{23}}{32}
=-\frac{\sqrt{23}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{23}}{2*16}=\frac{0+8\sqrt{23}}{32}
=\frac{8\sqrt{23}}{32}
=\frac{\sqrt{23}}{4}
$