(5/3)x=14-x^2

Solution for (5/3)x=14-x^2 equation:

(5/3)x=14-x^2

We move all terms to the left:

(5/3)x-(14-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

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

We multiply parentheses

-(14-x^2)+5x^2=0

We get rid of parentheses

x^2+5x^2-14=0

We add all the numbers together, and all the variables

6x^2-14=0

a = 6; b = 0; c = -14;
Δ = b2-4ac
Δ = 02-4·6·(-14)
Δ = 336
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:

$\sqrt{\Delta}=\sqrt{336}=\sqrt{16*21}=\sqrt{16}*\sqrt{21}=4\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{21}}{2*6}=\frac{0-4\sqrt{21}}{12}
=-\frac{4\sqrt{21}}{12}
=-\frac{\sqrt{21}}{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{21}}{2*6}=\frac{0+4\sqrt{21}}{12}
=\frac{4\sqrt{21}}{12}
=\frac{\sqrt{21}}{3}
$