27-x^2/4=0

Solution for 27-x^2/4=0 equation:

27-x^2/4=0

We multiply all the terms by the denominator


-x^2+27*4=0

We add all the numbers together, and all the variables

-1x^2+108=0

a = -1; b = 0; c = +108;
Δ = b2-4ac
Δ = 02-4·(-1)·108
Δ = 432
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:

$\sqrt{\Delta}=\sqrt{432}=\sqrt{144*3}=\sqrt{144}*\sqrt{3}=12\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{3}}{2*-1}=\frac{0-12\sqrt{3}}{-2}
=-\frac{12\sqrt{3}}{-2}
=-\frac{6\sqrt{3}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{3}}{2*-1}=\frac{0+12\sqrt{3}}{-2}
=\frac{12\sqrt{3}}{-2}
=\frac{6\sqrt{3}}{-1}
$