2=12x^2+5x

Solution for 2=12x^2+5x equation:

2=12x^2+5x

We move all terms to the left:

2-(12x^2+5x)=0

We get rid of parentheses

-12x^2-5x+2=0

a = -12; b = -5; c = +2;
Δ = b2-4ac
Δ = -52-4·(-12)·2
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-11}{2*-12}=\frac{-6}{-24}
=1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+11}{2*-12}=\frac{16}{-24}
=-2/3
$