1/2x+1/3x-7=5/6

Solution for 1/2x+1/3x-7=5/6 equation:

1/2x+1/3x-7=5/6

We move all terms to the left:

1/2x+1/3x-7-(5/6)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

1/2x+1/3x-7-(+5/6)=0

We get rid of parentheses

1/2x+1/3x-7-5/6=0

We calculate fractions


(-90x^2)/216x^2+108x/216x^2+72x/216x^2-7=0

We multiply all the terms by the denominator


(-90x^2)+108x+72x-7*216x^2=0

We add all the numbers together, and all the variables

(-90x^2)+180x-7*216x^2=0

Wy multiply elements

(-90x^2)-1512x^2+180x=0

We get rid of parentheses

-90x^2-1512x^2+180x=0

We add all the numbers together, and all the variables

-1602x^2+180x=0

a = -1602; b = 180; c = 0;
Δ = b2-4ac
Δ = 1802-4·(-1602)·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*-1602}=\frac{-360}{-3204}
=10/89
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(180)+180}{2*-1602}=\frac{0}{-3204}
=0
$