1/2x+5-8/x+4=-5

Solution for 1/2x+5-8/x+4=-5 equation:

1/2x+5-8/x+4=-5

We move all terms to the left:

1/2x+5-8/x+4-(-5)=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

1/2x-8/x+14=0

We calculate fractions


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

We multiply all the terms by the denominator


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

Wy multiply elements

28x^2+x+(-16x)=0

We get rid of parentheses

28x^2+x-16x=0

We add all the numbers together, and all the variables

28x^2-15x=0

a = 28; b = -15; c = 0;
Δ = b2-4ac
Δ = -152-4·28·0
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-15}{2*28}=\frac{0}{56}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+15}{2*28}=\frac{30}{56}
=15/28
$