12w^2+51w=-12

Solution for 12w^2+51w=-12 equation:

12w^2+51w=-12

We move all terms to the left:

12w^2+51w-(-12)=0

We add all the numbers together, and all the variables

12w^2+51w+12=0

a = 12; b = 51; c = +12;
Δ = b2-4ac
Δ = 512-4·12·12
Δ = 2025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2025}=45$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(51)-45}{2*12}=\frac{-96}{24}
=-4
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(51)+45}{2*12}=\frac{-6}{24}
=-1/4
$