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

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

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

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

We add all the numbers together, and all the variables

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

We multiply parentheses

0x^2+30x+3x*x-8.5x+15=0

Wy multiply elements

0x^2+3x^2+30x-8.5x+15=0

We add all the numbers together, and all the variables

4x^2+21.5x+15=0

a = 4; b = 21.5; c = +15;
Δ = b2-4ac
Δ = 21.52-4·4·15
Δ = 222.25
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{-(21.5)-\sqrt{222.25}}{2*4}=\frac{-21.5-\sqrt{222.25}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21.5)+\sqrt{222.25}}{2*4}=\frac{-21.5+\sqrt{222.25}}{8}
$