3x+15/x+30=-0.05+8.5

Solution for 3x+15/x+30=-0.05+8.5 equation:

3x+15/x+30=-0.05+8.5

We move all terms to the left:

3x+15/x+30-(-0.05+8.5)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

3x+15/x+30-(8.45)=0

We add all the numbers together, and all the variables

3x+15/x+21.55=0

We multiply all the terms by the denominator


3x*x+(21.55)*x+15=0

We multiply parentheses

3x*x+21.55x+15=0

Wy multiply elements

3x^2+21.55x+15=0

a = 3; b = 21.55; c = +15;
Δ = b2-4ac
Δ = 21.552-4·3·15
Δ = 284.4025
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{-(21.55)-\sqrt{284.4025}}{2*3}=\frac{-21.55-\sqrt{284.4025}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21.55)+\sqrt{284.4025}}{2*3}=\frac{-21.55+\sqrt{284.4025}}{6}
$