12x^+9=6x^2-16

Solution for 12x^+9=6x^2-16 equation:

12x^+9=6x^2-16

We move all terms to the left:

12x^+9-(6x^2-16)=0

We add all the numbers together, and all the variables

12x-(6x^2-16)+9=0

We get rid of parentheses

-6x^2+12x+16+9=0

We add all the numbers together, and all the variables

-6x^2+12x+25=0

a = -6; b = 12; c = +25;
Δ = b2-4ac
Δ = 122-4·(-6)·25
Δ = 744
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:

$\sqrt{\Delta}=\sqrt{744}=\sqrt{4*186}=\sqrt{4}*\sqrt{186}=2\sqrt{186}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-2\sqrt{186}}{2*-6}=\frac{-12-2\sqrt{186}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2\sqrt{186}}{2*-6}=\frac{-12+2\sqrt{186}}{-12}
$