(4/3x)(x)=4800

Solution for (4/3x)(x)=4800 equation:

(4/3x)(x)=4800

We move all terms to the left:

(4/3x)(x)-(4800)=0


Domain of the equation: 3x)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+4/3x)x-4800=0

We multiply parentheses

4x^2-4800=0

a = 4; b = 0; c = -4800;
Δ = b2-4ac
Δ = 02-4·4·(-4800)
Δ = 76800
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:

$\sqrt{\Delta}=\sqrt{76800}=\sqrt{25600*3}=\sqrt{25600}*\sqrt{3}=160\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-160\sqrt{3}}{2*4}=\frac{0-160\sqrt{3}}{8}
=-\frac{160\sqrt{3}}{8}
=-20\sqrt{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+160\sqrt{3}}{2*4}=\frac{0+160\sqrt{3}}{8}
=\frac{160\sqrt{3}}{8}
=20\sqrt{3}
$