12x+16=9x^2-16

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

12x+16=9x^2-16

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-9x^2+12x+32=0

a = -9; b = 12; c = +32;
Δ = b2-4ac
Δ = 122-4·(-9)·32
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-36}{2*-9}=\frac{-48}{-18}
=2+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+36}{2*-9}=\frac{24}{-18}
=-1+1/3
$