7/4x-2/3x=5/6

Solution for 7/4x-2/3x=5/6 equation:

7/4x-2/3x=5/6

We move all terms to the left:

7/4x-2/3x-(5/6)=0


Domain of the equation: 4x!=0

x!=0/4

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

7/4x-2/3x-(+5/6)=0

We get rid of parentheses

7/4x-2/3x-5/6=0

We calculate fractions


(-180x^2)/432x^2+756x/432x^2+(-288x)/432x^2=0

We multiply all the terms by the denominator


(-180x^2)+756x+(-288x)=0

We get rid of parentheses

-180x^2+756x-288x=0

We add all the numbers together, and all the variables

-180x^2+468x=0

a = -180; b = 468; c = 0;
Δ = b2-4ac
Δ = 4682-4·(-180)·0
Δ = 219024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{219024}=468$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(468)-468}{2*-180}=\frac{-936}{-360}
=2+3/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(468)+468}{2*-180}=\frac{0}{-360}
=0
$