-3x^2+11=-38

Solution for -3x^2+11=-38 equation:

-3x^2+11=-38

We move all terms to the left:

-3x^2+11-(-38)=0

We add all the numbers together, and all the variables

-3x^2+49=0

a = -3; b = 0; c = +49;
Δ = b2-4ac
Δ = 02-4·(-3)·49
Δ = 588
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:

$\sqrt{\Delta}=\sqrt{588}=\sqrt{196*3}=\sqrt{196}*\sqrt{3}=14\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-14\sqrt{3}}{2*-3}=\frac{0-14\sqrt{3}}{-6}
=-\frac{14\sqrt{3}}{-6}
=-\frac{7\sqrt{3}}{-3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+14\sqrt{3}}{2*-3}=\frac{0+14\sqrt{3}}{-6}
=\frac{14\sqrt{3}}{-6}
=\frac{7\sqrt{3}}{-3}
$