21x+3/6x+11=8/2

Solution for 21x+3/6x+11=8/2 equation:

21x+3/6x+11=8/2

We move all terms to the left:

21x+3/6x+11-(8/2)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We add all the numbers together, and all the variables

21x+3/6x+11-4=0

We add all the numbers together, and all the variables

21x+3/6x+7=0

We multiply all the terms by the denominator


21x*6x+7*6x+3=0

Wy multiply elements

126x^2+42x+3=0

a = 126; b = 42; c = +3;
Δ = b2-4ac
Δ = 422-4·126·3
Δ = 252
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:

$\sqrt{\Delta}=\sqrt{252}=\sqrt{36*7}=\sqrt{36}*\sqrt{7}=6\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(42)-6\sqrt{7}}{2*126}=\frac{-42-6\sqrt{7}}{252}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(42)+6\sqrt{7}}{2*126}=\frac{-42+6\sqrt{7}}{252}
$