3/x+2x-10=20

Solution for 3/x+2x-10=20 equation:

3/x+2x-10=20

We move all terms to the left:

3/x+2x-10-(20)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

2x+3/x-30=0

We multiply all the terms by the denominator


2x*x-30*x+3=0

We add all the numbers together, and all the variables

-30x+2x*x+3=0

Wy multiply elements

2x^2-30x+3=0

a = 2; b = -30; c = +3;
Δ = b2-4ac
Δ = -302-4·2·3
Δ = 876
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{876}=\sqrt{4*219}=\sqrt{4}*\sqrt{219}=2\sqrt{219}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-2\sqrt{219}}{2*2}=\frac{30-2\sqrt{219}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+2\sqrt{219}}{2*2}=\frac{30+2\sqrt{219}}{4}
$