1/2x+7/6x=25/3

Solution for 1/2x+7/6x=25/3 equation:

1/2x+7/6x=25/3

We move all terms to the left:

1/2x+7/6x-(25/3)=0


Domain of the equation: 2x!=0

x!=0/2

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

1/2x+7/6x-(+25/3)=0

We get rid of parentheses

1/2x+7/6x-25/3=0

We calculate fractions


(-1800x^2)/108x^2+54x/108x^2+126x/108x^2=0

We multiply all the terms by the denominator


(-1800x^2)+54x+126x=0

We add all the numbers together, and all the variables

(-1800x^2)+180x=0

We get rid of parentheses

-1800x^2+180x=0

a = -1800; b = 180; c = 0;
Δ = b2-4ac
Δ = 1802-4·(-1800)·0
Δ = 32400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{32400}=180$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(180)-180}{2*-1800}=\frac{-360}{-3600}
=1/10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(180)+180}{2*-1800}=\frac{0}{-3600}
=0
$