4x/x-7)=7/8

Solution for 4x/x-7)=7/8 equation:

4x/x-7)=7/8

We move all terms to the left:

4x/x-7)-(7/8)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

4x/x-7)-(+7/8)=0

We add all the numbers together, and all the variables

4x/x+7/8)=0

We calculate fractions


32x^2/8x^2+7x/8x^2=0

We multiply all the terms by the denominator


32x^2+7x=0

a = 32; b = 7; c = 0;
Δ = b2-4ac
Δ = 72-4·32·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-7}{2*32}=\frac{-14}{64}
=-7/32
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7}{2*32}=\frac{0}{64}
=0
$