12x2+72x+55=0

Solution for 12x2+72x+55=0 equation:

12x^2+72x+55=0

a = 12; b = 72; c = +55;
Δ = b2-4ac
Δ = 722-4·12·55
Δ = 2544
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:

$\sqrt{\Delta}=\sqrt{2544}=\sqrt{16*159}=\sqrt{16}*\sqrt{159}=4\sqrt{159}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(72)-4\sqrt{159}}{2*12}=\frac{-72-4\sqrt{159}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(72)+4\sqrt{159}}{2*12}=\frac{-72+4\sqrt{159}}{24}
$