10b^2+31b+12=-3

Solution for 10b^2+31b+12=-3 equation:

10b^2+31b+12=-3

We move all terms to the left:

10b^2+31b+12-(-3)=0

We add all the numbers together, and all the variables

10b^2+31b+15=0

a = 10; b = 31; c = +15;
Δ = b2-4ac
Δ = 312-4·10·15
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(31)-19}{2*10}=\frac{-50}{20}
=-2+1/2
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(31)+19}{2*10}=\frac{-12}{20}
=-3/5
$