12x2=2(6x+1)

Solution for 12x2=2(6x+1) equation:

12x^2=2(6x+1)

We move all terms to the left:

12x^2-(2(6x+1))=0


We calculate terms in parentheses: -(2(6x+1)), so:

2(6x+1)

We multiply parentheses

12x+2

Back to the equation:

-(12x+2)


We get rid of parentheses

12x^2-12x-2=0

a = 12; b = -12; c = -2;
Δ = b2-4ac
Δ = -122-4·12·(-2)
Δ = 240
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{240}=\sqrt{16*15}=\sqrt{16}*\sqrt{15}=4\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{15}}{2*12}=\frac{12-4\sqrt{15}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{15}}{2*12}=\frac{12+4\sqrt{15}}{24}
$