15x^2-27-6=0

Solution for 15x^2-27-6=0 equation:

15x^2-27-6=0

We add all the numbers together, and all the variables

15x^2-33=0

a = 15; b = 0; c = -33;
Δ = b2-4ac
Δ = 02-4·15·(-33)
Δ = 1980
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:

$\sqrt{\Delta}=\sqrt{1980}=\sqrt{36*55}=\sqrt{36}*\sqrt{55}=6\sqrt{55}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{55}}{2*15}=\frac{0-6\sqrt{55}}{30}
=-\frac{6\sqrt{55}}{30}
=-\frac{\sqrt{55}}{5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{55}}{2*15}=\frac{0+6\sqrt{55}}{30}
=\frac{6\sqrt{55}}{30}
=\frac{\sqrt{55}}{5}
$