2/3x+1/6x+4=19

Solution for 2/3x+1/6x+4=19 equation:

2/3x+1/6x+4=19

We move all terms to the left:

2/3x+1/6x+4-(19)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We add all the numbers together, and all the variables

2/3x+1/6x-15=0

We calculate fractions


12x/18x^2+3x/18x^2-15=0

We multiply all the terms by the denominator


12x+3x-15*18x^2=0

We add all the numbers together, and all the variables

15x-15*18x^2=0

Wy multiply elements

-270x^2+15x=0

a = -270; b = 15; c = 0;
Δ = b2-4ac
Δ = 152-4·(-270)·0
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-15}{2*-270}=\frac{-30}{-540}
=1/18
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+15}{2*-270}=\frac{0}{-540}
=0
$