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

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

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

We move all terms to the left:

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


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 6x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


180x^2/120x^2+72x/120x^2+(-140x)/120x^2=0

We multiply all the terms by the denominator


180x^2+72x+(-140x)=0

We get rid of parentheses

180x^2+72x-140x=0

We add all the numbers together, and all the variables

180x^2-68x=0

a = 180; b = -68; c = 0;
Δ = b2-4ac
Δ = -682-4·180·0
Δ = 4624
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4624}=68$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-68)-68}{2*180}=\frac{0}{360}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-68)+68}{2*180}=\frac{136}{360}
=17/45
$