4-12x2=13x

Solution for 4-12x2=13x equation:

4-12x^2=13x

We move all terms to the left:

4-12x^2-(13x)=0

a = -12; b = -13; c = +4;
Δ = b2-4ac
Δ = -132-4·(-12)·4
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-19}{2*-12}=\frac{-6}{-24}
=1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+19}{2*-12}=\frac{32}{-24}
=-1+1/3
$