15/2x+1+10/x=55/2

Solution for 15/2x+1+10/x=55/2 equation:

15/2x+1+10/x=55/2

We move all terms to the left:

15/2x+1+10/x-(55/2)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

15/2x+10/x+1-(+55/2)=0

We get rid of parentheses

15/2x+10/x+1-55/2=0

We calculate fractions


15x/8x^2+80x/8x^2+(-55x)/8x^2+1=0

We multiply all the terms by the denominator


15x+80x+(-55x)+1*8x^2=0

We add all the numbers together, and all the variables

95x+(-55x)+1*8x^2=0

Wy multiply elements

8x^2+95x+(-55x)=0

We get rid of parentheses

8x^2+95x-55x=0

We add all the numbers together, and all the variables

8x^2+40x=0

a = 8; b = 40; c = 0;
Δ = b2-4ac
Δ = 402-4·8·0
Δ = 1600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1600}=40$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-40}{2*8}=\frac{-80}{16}
=-5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+40}{2*8}=\frac{0}{16}
=0
$