6a^2+38a+12=0

Solution for 6a^2+38a+12=0 equation:

6a^2+38a+12=0

a = 6; b = 38; c = +12;
Δ = b2-4ac
Δ = 382-4·6·12
Δ = 1156
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1156}=34$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(38)-34}{2*6}=\frac{-72}{12}
=-6
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(38)+34}{2*6}=\frac{-4}{12}
=-1/3
$