1/3x+4=5x-1

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

1/3x+4=5x-1

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

1/3x-5x+1+4=0

We multiply all the terms by the denominator


-5x*3x+1*3x+4*3x+1=0

Wy multiply elements

-15x^2+3x+12x+1=0

We add all the numbers together, and all the variables

-15x^2+15x+1=0

a = -15; b = 15; c = +1;
Δ = b2-4ac
Δ = 152-4·(-15)·1
Δ = 285
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{-(15)-\sqrt{285}}{2*-15}=\frac{-15-\sqrt{285}}{-30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+\sqrt{285}}{2*-15}=\frac{-15+\sqrt{285}}{-30}
$