2x+(2/7x+1)+4x-(3x+2)=11+2

Solution for 2x+(2/7x+1)+4x-(3x+2)=11+2 equation:

2x+(2/7x+1)+4x-(3x+2)=11+2

We move all terms to the left:

2x+(2/7x+1)+4x-(3x+2)-(11+2)=0


Domain of the equation: 7x+1)!=0

x∈R


We add all the numbers together, and all the variables

2x+(2/7x+1)+4x-(3x+2)-13=0

We add all the numbers together, and all the variables

6x+(2/7x+1)-(3x+2)-13=0

We get rid of parentheses

6x+2/7x-3x+1-2-13=0

We multiply all the terms by the denominator


6x*7x-3x*7x+1*7x-2*7x-13*7x+2=0

Wy multiply elements

42x^2-21x^2+7x-14x-91x+2=0

We add all the numbers together, and all the variables

21x^2-98x+2=0

a = 21; b = -98; c = +2;
Δ = b2-4ac
Δ = -982-4·21·2
Δ = 9436
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:

$\sqrt{\Delta}=\sqrt{9436}=\sqrt{4*2359}=\sqrt{4}*\sqrt{2359}=2\sqrt{2359}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-98)-2\sqrt{2359}}{2*21}=\frac{98-2\sqrt{2359}}{42}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-98)+2\sqrt{2359}}{2*21}=\frac{98+2\sqrt{2359}}{42}
$