(3x^2)/16=33

Solution for (3x^2)/16=33 equation:

(3x^2)/16=33

We move all terms to the left:

(3x^2)/16-(33)=0

We multiply all the terms by the denominator


3x^2-33*16=0

We add all the numbers together, and all the variables

3x^2-528=0

a = 3; b = 0; c = -528;
Δ = b2-4ac
Δ = 02-4·3·(-528)
Δ = 6336
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:

$\sqrt{\Delta}=\sqrt{6336}=\sqrt{576*11}=\sqrt{576}*\sqrt{11}=24\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-24\sqrt{11}}{2*3}=\frac{0-24\sqrt{11}}{6}
=-\frac{24\sqrt{11}}{6}
=-4\sqrt{11}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+24\sqrt{11}}{2*3}=\frac{0+24\sqrt{11}}{6}
=\frac{24\sqrt{11}}{6}
=4\sqrt{11}
$