x^2-6/5=2

Solution for x^2-6/5=2 equation:

x^2-6/5=2

We move all terms to the left:

x^2-6/5-(2)=0

determiningTheFunctionDomain
x^2-2-6/5=0

We multiply all the terms by the denominator


x^2*5-6-2*5=0

We add all the numbers together, and all the variables

x^2*5-16=0

Wy multiply elements

5x^2-16=0

a = 5; b = 0; c = -16;
Δ = b2-4ac
Δ = 02-4·5·(-16)
Δ = 320
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:

$\sqrt{\Delta}=\sqrt{320}=\sqrt{64*5}=\sqrt{64}*\sqrt{5}=8\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{5}}{2*5}=\frac{0-8\sqrt{5}}{10}
=-\frac{8\sqrt{5}}{10}
=-\frac{4\sqrt{5}}{5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{5}}{2*5}=\frac{0+8\sqrt{5}}{10}
=\frac{8\sqrt{5}}{10}
=\frac{4\sqrt{5}}{5}
$