27/16=x^2

Solution for 27/16=x^2 equation:

27/16=x^2

We move all terms to the left:

27/16-(x^2)=0

We add all the numbers together, and all the variables

-1x^2+27/16=0

We multiply all the terms by the denominator


-1x^2*16+27=0

Wy multiply elements

-16x^2+27=0

a = -16; b = 0; c = +27;
Δ = b2-4ac
Δ = 02-4·(-16)·27
Δ = 1728
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:

$\sqrt{\Delta}=\sqrt{1728}=\sqrt{576*3}=\sqrt{576}*\sqrt{3}=24\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-24\sqrt{3}}{2*-16}=\frac{0-24\sqrt{3}}{-32}
=-\frac{24\sqrt{3}}{-32}
=-\frac{3\sqrt{3}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+24\sqrt{3}}{2*-16}=\frac{0+24\sqrt{3}}{-32}
=\frac{24\sqrt{3}}{-32}
=\frac{3\sqrt{3}}{-4}
$