14-3x^2=-5

Solution for 14-3x^2=-5 equation:

14-3x^2=-5

We move all terms to the left:

14-3x^2-(-5)=0

We add all the numbers together, and all the variables

-3x^2+19=0

a = -3; b = 0; c = +19;
Δ = b2-4ac
Δ = 02-4·(-3)·19
Δ = 228
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:

$\sqrt{\Delta}=\sqrt{228}=\sqrt{4*57}=\sqrt{4}*\sqrt{57}=2\sqrt{57}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{57}}{2*-3}=\frac{0-2\sqrt{57}}{-6}
=-\frac{2\sqrt{57}}{-6}
=-\frac{\sqrt{57}}{-3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{57}}{2*-3}=\frac{0+2\sqrt{57}}{-6}
=\frac{2\sqrt{57}}{-6}
=\frac{\sqrt{57}}{-3}
$