12w^2+46w-8=0

Solution for 12w^2+46w-8=0 equation:

12w^2+46w-8=0

a = 12; b = 46; c = -8;
Δ = b2-4ac
Δ = 462-4·12·(-8)
Δ = 2500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2500}=50$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(46)-50}{2*12}=\frac{-96}{24}
=-4
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(46)+50}{2*12}=\frac{4}{24}
=1/6
$