x=-3x^2+2x/14

Solution for x=-3x^2+2x/14 equation:

x=-3x^2+2x/14

We move all terms to the left:

x-(-3x^2+2x/14)=0

We get rid of parentheses

3x^2-2x/14+x=0

We multiply all the terms by the denominator


3x^2*14-2x+x*14=0

Wy multiply elements

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

We add all the numbers together, and all the variables

42x^2+12x=0

a = 42; b = 12; c = 0;
Δ = b2-4ac
Δ = 122-4·42·0
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-12}{2*42}=\frac{-24}{84}
=-2/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+12}{2*42}=\frac{0}{84}
=0
$