4/3x+6+x=118

Solution for 4/3x+6+x=118 equation:

4/3x+6+x=118

We move all terms to the left:

4/3x+6+x-(118)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

x+4/3x-112=0

We multiply all the terms by the denominator


x*3x-112*3x+4=0

Wy multiply elements

3x^2-336x+4=0

a = 3; b = -336; c = +4;
Δ = b2-4ac
Δ = -3362-4·3·4
Δ = 112848
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:

$\sqrt{\Delta}=\sqrt{112848}=\sqrt{16*7053}=\sqrt{16}*\sqrt{7053}=4\sqrt{7053}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-336)-4\sqrt{7053}}{2*3}=\frac{336-4\sqrt{7053}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-336)+4\sqrt{7053}}{2*3}=\frac{336+4\sqrt{7053}}{6}
$