6/5x-7=14x

Solution for 6/5x-7=14x equation:

6/5x-7=14x

We move all terms to the left:

6/5x-7-(14x)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

-14x+6/5x-7=0

We multiply all the terms by the denominator


-14x*5x-7*5x+6=0

Wy multiply elements

-70x^2-35x+6=0

a = -70; b = -35; c = +6;
Δ = b2-4ac
Δ = -352-4·(-70)·6
Δ = 2905
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-35)-\sqrt{2905}}{2*-70}=\frac{35-\sqrt{2905}}{-140}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-35)+\sqrt{2905}}{2*-70}=\frac{35+\sqrt{2905}}{-140}
$