3x+10/2x+20=2/1

Solution for 3x+10/2x+20=2/1 equation:

3x+10/2x+20=2/1

We move all terms to the left:

3x+10/2x+20-(2/1)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

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

We add all the numbers together, and all the variables

3x+10/2x+20=0

We multiply all the terms by the denominator


3x*2x+20*2x+10=0

Wy multiply elements

6x^2+40x+10=0

a = 6; b = 40; c = +10;
Δ = b2-4ac
Δ = 402-4·6·10
Δ = 1360
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:

$\sqrt{\Delta}=\sqrt{1360}=\sqrt{16*85}=\sqrt{16}*\sqrt{85}=4\sqrt{85}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-4\sqrt{85}}{2*6}=\frac{-40-4\sqrt{85}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+4\sqrt{85}}{2*6}=\frac{-40+4\sqrt{85}}{12}
$