5x+7/8+2x/x+5=x

Solution for 5x+7/8+2x/x+5=x equation:

5x+7/8+2x/x+5=x

We move all terms to the left:

5x+7/8+2x/x+5-(x)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

4x+2x/x+5+7/8=0

We calculate fractions


4x+16x/8x+7x/8x+5=0

We multiply all the terms by the denominator


4x*8x+16x+7x+5*8x=0

We add all the numbers together, and all the variables

23x+4x*8x+5*8x=0

Wy multiply elements

32x^2+23x+40x=0

We add all the numbers together, and all the variables

32x^2+63x=0

a = 32; b = 63; c = 0;
Δ = b2-4ac
Δ = 632-4·32·0
Δ = 3969
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3969}=63$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(63)-63}{2*32}=\frac{-126}{64}
=-1+31/32
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(63)+63}{2*32}=\frac{0}{64}
=0
$