1/3x+5=4x-2

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

1/3x+5=4x-2

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


-4x*3x+2*3x+5*3x+1=0

Wy multiply elements

-12x^2+6x+15x+1=0

We add all the numbers together, and all the variables

-12x^2+21x+1=0

a = -12; b = 21; c = +1;
Δ = b2-4ac
Δ = 212-4·(-12)·1
Δ = 489
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{-(21)-\sqrt{489}}{2*-12}=\frac{-21-\sqrt{489}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+\sqrt{489}}{2*-12}=\frac{-21+\sqrt{489}}{-24}
$