1/3x+4=32x+3

Solution for 1/3x+4=32x+3 equation:

1/3x+4=32x+3

We move all terms to the left:

1/3x+4-(32x+3)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

1/3x-32x-3+4=0

We multiply all the terms by the denominator


-32x*3x-3*3x+4*3x+1=0

Wy multiply elements

-96x^2-9x+12x+1=0

We add all the numbers together, and all the variables

-96x^2+3x+1=0

a = -96; b = 3; c = +1;
Δ = b2-4ac
Δ = 32-4·(-96)·1
Δ = 393
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{-(3)-\sqrt{393}}{2*-96}=\frac{-3-\sqrt{393}}{-192}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{393}}{2*-96}=\frac{-3+\sqrt{393}}{-192}
$