2/3x+2/6x+5=10

Solution for 2/3x+2/6x+5=10 equation:

2/3x+2/6x+5=10

We move all terms to the left:

2/3x+2/6x+5-(10)=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+2/6x-5=0

We calculate fractions


12x/18x^2+6x/18x^2-5=0

We multiply all the terms by the denominator


12x+6x-5*18x^2=0

We add all the numbers together, and all the variables

18x-5*18x^2=0

Wy multiply elements

-90x^2+18x=0

a = -90; b = 18; c = 0;
Δ = b2-4ac
Δ = 182-4·(-90)·0
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-18}{2*-90}=\frac{-36}{-180}
=1/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+18}{2*-90}=\frac{0}{-180}
=0
$