5x-2/3x+4=1

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

5x-2/3x+4=1

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

5x-2/3x+3=0

We multiply all the terms by the denominator


5x*3x+3*3x-2=0

Wy multiply elements

15x^2+9x-2=0

a = 15; b = 9; c = -2;
Δ = b2-4ac
Δ = 92-4·15·(-2)
Δ = 201
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-\sqrt{201}}{2*15}=\frac{-9-\sqrt{201}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{201}}{2*15}=\frac{-9+\sqrt{201}}{30}
$