3x^2-5x-31=-3

Solution for 3x^2-5x-31=-3 equation:

3x^2-5x-31=-3

We move all terms to the left:

3x^2-5x-31-(-3)=0

We add all the numbers together, and all the variables

3x^2-5x-28=0

a = 3; b = -5; c = -28;
Δ = b2-4ac
Δ = -52-4·3·(-28)
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-19}{2*3}=\frac{-14}{6}
=-2+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+19}{2*3}=\frac{24}{6}
=4
$