2x^2+7/3=13

Solution for 2x^2+7/3=13 equation:

2x^2+7/3=13

We move all terms to the left:

2x^2+7/3-(13)=0

determiningTheFunctionDomain
2x^2-13+7/3=0

We multiply all the terms by the denominator


2x^2*3+7-13*3=0

We add all the numbers together, and all the variables

2x^2*3-32=0

Wy multiply elements

6x^2-32=0

a = 6; b = 0; c = -32;
Δ = b2-4ac
Δ = 02-4·6·(-32)
Δ = 768
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:

$\sqrt{\Delta}=\sqrt{768}=\sqrt{256*3}=\sqrt{256}*\sqrt{3}=16\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-16\sqrt{3}}{2*6}=\frac{0-16\sqrt{3}}{12}
=-\frac{16\sqrt{3}}{12}
=-\frac{4\sqrt{3}}{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+16\sqrt{3}}{2*6}=\frac{0+16\sqrt{3}}{12}
=\frac{16\sqrt{3}}{12}
=\frac{4\sqrt{3}}{3}
$