x+2(3x^2-5)=12x

Solution for x+2(3x^2-5)=12x equation:

x+2(3x^2-5)=12x

We move all terms to the left:

x+2(3x^2-5)-(12x)=0

We add all the numbers together, and all the variables

-11x+2(3x^2-5)=0

We multiply parentheses

6x^2-11x-10=0

a = 6; b = -11; c = -10;
Δ = b2-4ac
Δ = -112-4·6·(-10)
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{-(-11)-19}{2*6}=\frac{-8}{12}
=-2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+19}{2*6}=\frac{30}{12}
=2+1/2
$