3x+5/6x+10=20

Solution for 3x+5/6x+10=20 equation:

3x+5/6x+10=20

We move all terms to the left:

3x+5/6x+10-(20)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We add all the numbers together, and all the variables

3x+5/6x-10=0

We multiply all the terms by the denominator


3x*6x-10*6x+5=0

Wy multiply elements

18x^2-60x+5=0

a = 18; b = -60; c = +5;
Δ = b2-4ac
Δ = -602-4·18·5
Δ = 3240
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:

$\sqrt{\Delta}=\sqrt{3240}=\sqrt{324*10}=\sqrt{324}*\sqrt{10}=18\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-18\sqrt{10}}{2*18}=\frac{60-18\sqrt{10}}{36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+18\sqrt{10}}{2*18}=\frac{60+18\sqrt{10}}{36}
$