14x=16(x-1/6)

Solution for 14x=16(x-1/6) equation:

14x=16(x-1/6)

We move all terms to the left:

14x-(16(x-1/6))=0

We add all the numbers together, and all the variables

14x-(16(+x-1/6))=0

We multiply all the terms by the denominator


14x*6))-(16(+x-1=0

We add all the numbers together, and all the variables

x+14x*6))-(16(-1=0

Wy multiply elements

84x^2+x-1=0

a = 84; b = 1; c = -1;
Δ = b2-4ac
Δ = 12-4·84·(-1)
Δ = 337
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{-(1)-\sqrt{337}}{2*84}=\frac{-1-\sqrt{337}}{168}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{337}}{2*84}=\frac{-1+\sqrt{337}}{168}
$