12x^2-32x+9=0

Solution for 12x^2-32x+9=0 equation:

12x^2-32x+9=0

a = 12; b = -32; c = +9;
Δ = b2-4ac
Δ = -322-4·12·9
Δ = 592
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:

$\sqrt{\Delta}=\sqrt{592}=\sqrt{16*37}=\sqrt{16}*\sqrt{37}=4\sqrt{37}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-4\sqrt{37}}{2*12}=\frac{32-4\sqrt{37}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+4\sqrt{37}}{2*12}=\frac{32+4\sqrt{37}}{24}
$