6n^2-31n=-5

Solution for 6n^2-31n=-5 equation:

6n^2-31n=-5

We move all terms to the left:

6n^2-31n-(-5)=0

We add all the numbers together, and all the variables

6n^2-31n+5=0

a = 6; b = -31; c = +5;
Δ = b2-4ac
Δ = -312-4·6·5
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-31)-29}{2*6}=\frac{2}{12}
=1/6
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-31)+29}{2*6}=\frac{60}{12}
=5
$