3x^2+1=11/2

Solution for 3x^2+1=11/2 equation:

3x^2+1=11/2

We move all terms to the left:

3x^2+1-(11/2)=0

We add all the numbers together, and all the variables

3x^2+1-(+11/2)=0

We get rid of parentheses

3x^2+1-11/2=0

We multiply all the terms by the denominator


3x^2*2-11+1*2=0

We add all the numbers together, and all the variables

3x^2*2-9=0

Wy multiply elements

6x^2-9=0

a = 6; b = 0; c = -9;
Δ = b2-4ac
Δ = 02-4·6·(-9)
Δ = 216
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:

$\sqrt{\Delta}=\sqrt{216}=\sqrt{36*6}=\sqrt{36}*\sqrt{6}=6\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{6}}{2*6}=\frac{0-6\sqrt{6}}{12}
=-\frac{6\sqrt{6}}{12}
=-\frac{\sqrt{6}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{6}}{2*6}=\frac{0+6\sqrt{6}}{12}
=\frac{6\sqrt{6}}{12}
=\frac{\sqrt{6}}{2}
$