5x^2/3=x^2+24

Solution for 5x^2/3=x^2+24 equation:

5x^2/3=x^2+24

We move all terms to the left:

5x^2/3-(x^2+24)=0

We get rid of parentheses

5x^2/3-x^2-24=0

We multiply all the terms by the denominator


5x^2-x^2*3-24*3=0

We add all the numbers together, and all the variables

5x^2-x^2*3-72=0

Wy multiply elements

5x^2-3x^2-72=0

We add all the numbers together, and all the variables

2x^2-72=0

a = 2; b = 0; c = -72;
Δ = b2-4ac
Δ = 02-4·2·(-72)
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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