(4/3)x=44-x^2

Solution for (4/3)x=44-x^2 equation:

(4/3)x=44-x^2

We move all terms to the left:

(4/3)x-(44-x^2)=0


Domain of the equation: 3)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-(44-x^2)+(+4/3)x=0

We multiply parentheses

-(44-x^2)+4x^2=0

We get rid of parentheses

x^2+4x^2-44=0

We add all the numbers together, and all the variables

5x^2-44=0

a = 5; b = 0; c = -44;
Δ = b2-4ac
Δ = 02-4·5·(-44)
Δ = 880
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:

$\sqrt{\Delta}=\sqrt{880}=\sqrt{16*55}=\sqrt{16}*\sqrt{55}=4\sqrt{55}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{55}}{2*5}=\frac{0-4\sqrt{55}}{10}
=-\frac{4\sqrt{55}}{10}
=-\frac{2\sqrt{55}}{5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{55}}{2*5}=\frac{0+4\sqrt{55}}{10}
=\frac{4\sqrt{55}}{10}
=\frac{2\sqrt{55}}{5}
$