1/2x+7/12+3/5x=2/3

Solution for 1/2x+7/12+3/5x=2/3 equation:

1/2x+7/12+3/5x=2/3

We move all terms to the left:

1/2x+7/12+3/5x-(2/3)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

1/2x+3/5x+7/12-(+2/3)=0

We get rid of parentheses

1/2x+3/5x+7/12-2/3=0

We calculate fractions


(-1200x^2)/360x^2+1050x^2/360x^2+180x/360x^2+216x/360x^2=0

We multiply all the terms by the denominator


(-1200x^2)+1050x^2+180x+216x=0

We add all the numbers together, and all the variables

1050x^2+(-1200x^2)+396x=0

We get rid of parentheses

1050x^2-1200x^2+396x=0

We add all the numbers together, and all the variables

-150x^2+396x=0

a = -150; b = 396; c = 0;
Δ = b2-4ac
Δ = 3962-4·(-150)·0
Δ = 156816
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{156816}=396$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(396)-396}{2*-150}=\frac{-792}{-300}
=2+16/25
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(396)+396}{2*-150}=\frac{0}{-300}
=0
$