0.5+x=140/x-30

Solution for 0.5+x=140/x-30 equation:

0.5+x=140/x-30

We move all terms to the left:

0.5+x-(140/x-30)=0


Domain of the equation: x-30)!=0

x∈R


We get rid of parentheses

x-140/x+30+0.5=0

We multiply all the terms by the denominator


x*x+30*x+(0.5)*x-140=0

We add all the numbers together, and all the variables

30x+x*x+(0.5)*x-140=0

We multiply parentheses

30x+x*x+0.5x-140=0

Wy multiply elements

x^2+30x+0.5x-140=0

We add all the numbers together, and all the variables

x^2+30.5x-140=0

a = 1; b = 30.5; c = -140;
Δ = b2-4ac
Δ = 30.52-4·1·(-140)
Δ = 1490.25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30.5)-\sqrt{1490.25}}{2*1}=\frac{-30.5-\sqrt{1490.25}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30.5)+\sqrt{1490.25}}{2*1}=\frac{-30.5+\sqrt{1490.25}}{2}
$