6x+9=4x^2-12

Solution for 6x+9=4x^2-12 equation:

6x+9=4x^2-12

We move all terms to the left:

6x+9-(4x^2-12)=0

We get rid of parentheses

-4x^2+6x+12+9=0

We add all the numbers together, and all the variables

-4x^2+6x+21=0

a = -4; b = 6; c = +21;
Δ = b2-4ac
Δ = 62-4·(-4)·21
Δ = 372
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:

$\sqrt{\Delta}=\sqrt{372}=\sqrt{4*93}=\sqrt{4}*\sqrt{93}=2\sqrt{93}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{93}}{2*-4}=\frac{-6-2\sqrt{93}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{93}}{2*-4}=\frac{-6+2\sqrt{93}}{-8}
$