1/3x+4=4x+10

Solution for 1/3x+4=4x+10 equation:

1/3x+4=4x+10

We move all terms to the left:

1/3x+4-(4x+10)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

1/3x-4x-10+4=0

We multiply all the terms by the denominator


-4x*3x-10*3x+4*3x+1=0

Wy multiply elements

-12x^2-30x+12x+1=0

We add all the numbers together, and all the variables

-12x^2-18x+1=0

a = -12; b = -18; c = +1;
Δ = b2-4ac
Δ = -182-4·(-12)·1
Δ = 372
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:

$\sqrt{\Delta}=\sqrt{372}=\sqrt{4*93}=\sqrt{4}*\sqrt{93}=2\sqrt{93}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{93}}{2*-12}=\frac{18-2\sqrt{93}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{93}}{2*-12}=\frac{18+2\sqrt{93}}{-24}
$