12+4.x=9x2-2

Solution for 12+4.x=9x2-2 equation:

12+4.x=9x^2-2

We move all terms to the left:

12+4.x-(9x^2-2)=0

We get rid of parentheses

-9x^2+4.x+2+12=0

We add all the numbers together, and all the variables

-9x^2+4.x+14=0

a = -9; b = 4.; c = +14;
Δ = b2-4ac
Δ = 4.2-4·(-9)·14
Δ = 520
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:

$\sqrt{\Delta}=\sqrt{520}=\sqrt{4*130}=\sqrt{4}*\sqrt{130}=2\sqrt{130}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4.)-2\sqrt{130}}{2*-9}=\frac{-4-2\sqrt{130}}{-18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4.)+2\sqrt{130}}{2*-9}=\frac{-4+2\sqrt{130}}{-18}
$