7/2x-6=7/8x

Solution for 7/2x-6=7/8x equation:

7/2x-6=7/8x

We move all terms to the left:

7/2x-6-(7/8x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 8x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

7/2x-(+7/8x)-6=0

We get rid of parentheses

7/2x-7/8x-6=0

We calculate fractions


56x/16x^2+(-14x)/16x^2-6=0

We multiply all the terms by the denominator


56x+(-14x)-6*16x^2=0

Wy multiply elements

-96x^2+56x+(-14x)=0

We get rid of parentheses

-96x^2+56x-14x=0

We add all the numbers together, and all the variables

-96x^2+42x=0

a = -96; b = 42; c = 0;
Δ = b2-4ac
Δ = 422-4·(-96)·0
Δ = 1764
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1764}=42$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(42)-42}{2*-96}=\frac{-84}{-192}
=7/16
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(42)+42}{2*-96}=\frac{0}{-192}
=0
$