6+8/14x=5x

Solution for 6+8/14x=5x equation:

6+8/14x=5x

We move all terms to the left:

6+8/14x-(5x)=0


Domain of the equation: 14x!=0

x!=0/14

x!=0

x∈R


We add all the numbers together, and all the variables

-5x+8/14x+6=0

We multiply all the terms by the denominator


-5x*14x+6*14x+8=0

Wy multiply elements

-70x^2+84x+8=0

a = -70; b = 84; c = +8;
Δ = b2-4ac
Δ = 842-4·(-70)·8
Δ = 9296
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:

$\sqrt{\Delta}=\sqrt{9296}=\sqrt{16*581}=\sqrt{16}*\sqrt{581}=4\sqrt{581}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(84)-4\sqrt{581}}{2*-70}=\frac{-84-4\sqrt{581}}{-140}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(84)+4\sqrt{581}}{2*-70}=\frac{-84+4\sqrt{581}}{-140}
$