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

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

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

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 6.x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


(-1008x^2)/48x^2+36x/48x^2+(-80x)/48x^2=0

We multiply all the terms by the denominator


(-1008x^2)+36x+(-80x)=0

We get rid of parentheses

-1008x^2+36x-80x=0

We add all the numbers together, and all the variables

-1008x^2-44x=0

a = -1008; b = -44; c = 0;
Δ = b2-4ac
Δ = -442-4·(-1008)·0
Δ = 1936
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1936}=44$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-44)-44}{2*-1008}=\frac{0}{-2016}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-44)+44}{2*-1008}=\frac{88}{-2016}
=-11/252
$