3/4x+2-1/6x=10

Solution for 3/4x+2-1/6x=10 equation:

3/4x+2-1/6x=10

We move all terms to the left:

3/4x+2-1/6x-(10)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We add all the numbers together, and all the variables

3/4x-1/6x-8=0

We calculate fractions


18x/24x^2+(-4x)/24x^2-8=0

We multiply all the terms by the denominator


18x+(-4x)-8*24x^2=0

Wy multiply elements

-192x^2+18x+(-4x)=0

We get rid of parentheses

-192x^2+18x-4x=0

We add all the numbers together, and all the variables

-192x^2+14x=0

a = -192; b = 14; c = 0;
Δ = b2-4ac
Δ = 142-4·(-192)·0
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-14}{2*-192}=\frac{-28}{-384}
=7/96
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+14}{2*-192}=\frac{0}{-384}
=0
$