x^2+5/8=2

Solution for x^2+5/8=2 equation:

x^2+5/8=2

We move all terms to the left:

x^2+5/8-(2)=0

determiningTheFunctionDomain
x^2-2+5/8=0

We multiply all the terms by the denominator


x^2*8+5-2*8=0

We add all the numbers together, and all the variables

x^2*8-11=0

Wy multiply elements

8x^2-11=0

a = 8; b = 0; c = -11;
Δ = b2-4ac
Δ = 02-4·8·(-11)
Δ = 352
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:

$\sqrt{\Delta}=\sqrt{352}=\sqrt{16*22}=\sqrt{16}*\sqrt{22}=4\sqrt{22}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{22}}{2*8}=\frac{0-4\sqrt{22}}{16}
=-\frac{4\sqrt{22}}{16}
=-\frac{\sqrt{22}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{22}}{2*8}=\frac{0+4\sqrt{22}}{16}
=\frac{4\sqrt{22}}{16}
=\frac{\sqrt{22}}{4}
$