14x=6-12x^2

Solution for 14x=6-12x^2 equation:

14x=6-12x^2

We move all terms to the left:

14x-(6-12x^2)=0

We get rid of parentheses

12x^2+14x-6=0

a = 12; b = 14; c = -6;
Δ = b2-4ac
Δ = 142-4·12·(-6)
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-22}{2*12}=\frac{-36}{24}
=-1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+22}{2*12}=\frac{8}{24}
=1/3
$