X2/x-3=7/3

Solution for X2/x-3=7/3 equation:

X2/X-3=7/3

We move all terms to the left:

X2/X-3-(7/3)=0


Domain of the equation: X!=0

X∈R


We add all the numbers together, and all the variables

X2/X-3-(+7/3)=0

We get rid of parentheses

X2/X-3-7/3=0

We calculate fractions


3X^2/3X+(-7X)/3X-3=0

We multiply all the terms by the denominator


3X^2+(-7X)-3*3X=0

Wy multiply elements

3X^2+(-7X)-9X=0

We get rid of parentheses

3X^2-7X-9X=0

We add all the numbers together, and all the variables

3X^2-16X=0

a = 3; b = -16; c = 0;
Δ = b2-4ac
Δ = -162-4·3·0
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-16}{2*3}=\frac{0}{6}
=0
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+16}{2*3}=\frac{32}{6}
=5+1/3
$