X^2/3x-1=4/5

Solution for X^2/3x-1=4/5 equation:

X^2/3X-1=4/5

We move all terms to the left:

X^2/3X-1-(4/5)=0


Domain of the equation: 3X!=0

X!=0/3

X!=0

X∈R


We add all the numbers together, and all the variables

X^2/3X-1-(+4/5)=0

We get rid of parentheses

X^2/3X-1-4/5=0

We calculate fractions


5X^2/15X+(-12X)/15X-1=0

We multiply all the terms by the denominator


5X^2+(-12X)-1*15X=0

Wy multiply elements

5X^2+(-12X)-15X=0

We get rid of parentheses

5X^2-12X-15X=0

We add all the numbers together, and all the variables

5X^2-27X=0

a = 5; b = -27; c = 0;
Δ = b2-4ac
Δ = -272-4·5·0
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-27}{2*5}=\frac{0}{10}
=0
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+27}{2*5}=\frac{54}{10}
=5+2/5
$