16/5=x^2

Solution for 16/5=x^2 equation:

16/5=x^2

We move all terms to the left:

16/5-(x^2)=0

We add all the numbers together, and all the variables

-1x^2+16/5=0

We multiply all the terms by the denominator


-1x^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}
$