14-13x=12x^2

Solution for 14-13x=12x^2 equation:

14-13x=12x^2

We move all terms to the left:

14-13x-(12x^2)=0

determiningTheFunctionDomain
-12x^2-13x+14=0

a = -12; b = -13; c = +14;
Δ = b2-4ac
Δ = -132-4·(-12)·14
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-29}{2*-12}=\frac{-16}{-24}
=2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+29}{2*-12}=\frac{42}{-24}
=-1+3/4
$