7x^2-27=0

Solution for 7x^2-27=0 equation:

7x^2-27=0

a = 7; b = 0; c = -27;
Δ = b2-4ac
Δ = 02-4·7·(-27)
Δ = 756
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:

$\sqrt{\Delta}=\sqrt{756}=\sqrt{36*21}=\sqrt{36}*\sqrt{21}=6\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{21}}{2*7}=\frac{0-6\sqrt{21}}{14}
=-\frac{6\sqrt{21}}{14}
=-\frac{3\sqrt{21}}{7}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{21}}{2*7}=\frac{0+6\sqrt{21}}{14}
=\frac{6\sqrt{21}}{14}
=\frac{3\sqrt{21}}{7}
$