2/7x+2x-5=6x

Solution for 2/7x+2x-5=6x equation:

2/7x+2x-5=6x

We move all terms to the left:

2/7x+2x-5-(6x)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R


We add all the numbers together, and all the variables

-4x+2/7x-5=0

We multiply all the terms by the denominator


-4x*7x-5*7x+2=0

Wy multiply elements

-28x^2-35x+2=0

a = -28; b = -35; c = +2;
Δ = b2-4ac
Δ = -352-4·(-28)·2
Δ = 1449
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:

$\sqrt{\Delta}=\sqrt{1449}=\sqrt{9*161}=\sqrt{9}*\sqrt{161}=3\sqrt{161}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-35)-3\sqrt{161}}{2*-28}=\frac{35-3\sqrt{161}}{-56}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-35)+3\sqrt{161}}{2*-28}=\frac{35+3\sqrt{161}}{-56}
$