8-3x^2=-25

Solution for 8-3x^2=-25 equation:

8-3x^2=-25

We move all terms to the left:

8-3x^2-(-25)=0

We add all the numbers together, and all the variables

-3x^2+33=0

a = -3; b = 0; c = +33;
Δ = b2-4ac
Δ = 02-4·(-3)·33
Δ = 396
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:

$\sqrt{\Delta}=\sqrt{396}=\sqrt{36*11}=\sqrt{36}*\sqrt{11}=6\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{11}}{2*-3}=\frac{0-6\sqrt{11}}{-6}
=-\frac{6\sqrt{11}}{-6}
=-\frac{\sqrt{11}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{11}}{2*-3}=\frac{0+6\sqrt{11}}{-6}
=\frac{6\sqrt{11}}{-6}
=\frac{\sqrt{11}}{-1}
$