3/4x-7/12x=1

Solution for 3/4x-7/12x=1 equation:

3/4x-7/12x=1

We move all terms to the left:

3/4x-7/12x-(1)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 12x!=0

x!=0/12

x!=0

x∈R


We calculate fractions


36x/48x^2+(-28x)/48x^2-1=0

We multiply all the terms by the denominator


36x+(-28x)-1*48x^2=0

Wy multiply elements

-48x^2+36x+(-28x)=0

We get rid of parentheses

-48x^2+36x-28x=0

We add all the numbers together, and all the variables

-48x^2+8x=0

a = -48; b = 8; c = 0;
Δ = b2-4ac
Δ = 82-4·(-48)·0
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-8}{2*-48}=\frac{-16}{-96}
=1/6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8}{2*-48}=\frac{0}{-96}
=0
$