5/7x+6=2x

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

5/7x+6=2x

We move all terms to the left:

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


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R


We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


-2x*7x+6*7x+5=0

Wy multiply elements

-14x^2+42x+5=0

a = -14; b = 42; c = +5;
Δ = b2-4ac
Δ = 422-4·(-14)·5
Δ = 2044
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:

$\sqrt{\Delta}=\sqrt{2044}=\sqrt{4*511}=\sqrt{4}*\sqrt{511}=2\sqrt{511}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(42)-2\sqrt{511}}{2*-14}=\frac{-42-2\sqrt{511}}{-28}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(42)+2\sqrt{511}}{2*-14}=\frac{-42+2\sqrt{511}}{-28}
$