(6/11)=3x^2

Solution for (6/11)=3x^2 equation:

(6/11)=3x^2

We move all terms to the left:

(6/11)-(3x^2)=0

We add all the numbers together, and all the variables

-3x^2+(+6/11)=0

We get rid of parentheses

-3x^2+6/11=0

We multiply all the terms by the denominator


-3x^2*11+6=0

Wy multiply elements

-33x^2+6=0

a = -33; b = 0; c = +6;
Δ = b2-4ac
Δ = 02-4·(-33)·6
Δ = 792
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:

$\sqrt{\Delta}=\sqrt{792}=\sqrt{36*22}=\sqrt{36}*\sqrt{22}=6\sqrt{22}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{22}}{2*-33}=\frac{0-6\sqrt{22}}{-66}
=-\frac{6\sqrt{22}}{-66}
=-\frac{\sqrt{22}}{-11}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{22}}{2*-33}=\frac{0+6\sqrt{22}}{-66}
=\frac{6\sqrt{22}}{-66}
=\frac{\sqrt{22}}{-11}
$