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

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

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

We move all terms to the left:

7/2x+5-1/3x-(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

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

We get rid of parentheses

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

We calculate fractions


(-90x^2)/216x^2+756x/216x^2+(-72x)/216x^2+5=0

We multiply all the terms by the denominator


(-90x^2)+756x+(-72x)+5*216x^2=0

Wy multiply elements

(-90x^2)+1080x^2+756x+(-72x)=0

We get rid of parentheses

-90x^2+1080x^2+756x-72x=0

We add all the numbers together, and all the variables

990x^2+684x=0

a = 990; b = 684; c = 0;
Δ = b2-4ac
Δ = 6842-4·990·0
Δ = 467856
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{467856}=684$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(684)-684}{2*990}=\frac{-1368}{1980}
=-38/55
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(684)+684}{2*990}=\frac{0}{1980}
=0
$