1/6x-3/4x+1/2=28

Solution for 1/6x-3/4x+1/2=28 equation:

1/6x-3/4x+1/2=28

We move all terms to the left:

1/6x-3/4x+1/2-(28)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R



Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


determiningTheFunctionDomain
1/6x-3/4x-28+1/2=0

We calculate fractions


96x^2/96x^2+16x/96x^2+(-72x)/96x^2-28=0

Fractions to decimals

16x/96x^2+(-72x)/96x^2-28+1=0

We multiply all the terms by the denominator


16x+(-72x)-28*96x^2+1*96x^2=0

Wy multiply elements

-2688x^2+96x^2+16x+(-72x)=0

We get rid of parentheses

-2688x^2+96x^2+16x-72x=0

We add all the numbers together, and all the variables

-2592x^2-56x=0

a = -2592; b = -56; c = 0;
Δ = b2-4ac
Δ = -562-4·(-2592)·0
Δ = 3136
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3136}=56$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-56)-56}{2*-2592}=\frac{0}{-5184}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-56)+56}{2*-2592}=\frac{112}{-5184}
=-7/324
$