5/3x2+8=2/3x2+57

Solution for 5/3x2+8=2/3x2+57 equation:

5/3x^2+8=2/3x^2+57

We move all terms to the left:

5/3x^2+8-(2/3x^2+57)=0


Domain of the equation: 3x^2!=0

x^2!=0/3

x^2!=√0

x!=0

x∈R



Domain of the equation: 3x^2+57)!=0

x∈R


We get rid of parentheses

5/3x^2-2/3x^2-57+8=0

We multiply all the terms by the denominator


-57*3x^2+8*3x^2+5-2=0

We add all the numbers together, and all the variables

-57*3x^2+8*3x^2+3=0

Wy multiply elements

-171x^2+24x^2+3=0

We add all the numbers together, and all the variables

-147x^2+3=0

a = -147; b = 0; c = +3;
Δ = b2-4ac
Δ = 02-4·(-147)·3
Δ = 1764
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1764}=42$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-42}{2*-147}=\frac{-42}{-294}
=1/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+42}{2*-147}=\frac{42}{-294}
=-1/7
$