5/3x+1=-1+5x

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

5/3x+1=-1+5x

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

5/3x-5x+1+1=0

We multiply all the terms by the denominator


-5x*3x+1*3x+1*3x+5=0

Wy multiply elements

-15x^2+3x+3x+5=0

We add all the numbers together, and all the variables

-15x^2+6x+5=0

a = -15; b = 6; c = +5;
Δ = b2-4ac
Δ = 62-4·(-15)·5
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{-(6)-4\sqrt{21}}{2*-15}=\frac{-6-4\sqrt{21}}{-30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+4\sqrt{21}}{2*-15}=\frac{-6+4\sqrt{21}}{-30}
$