-40c^2+31c=6

Solution for -40c^2+31c=6 equation:

-40c^2+31c=6

We move all terms to the left:

-40c^2+31c-(6)=0

a = -40; b = 31; c = -6;
Δ = b2-4ac
Δ = 312-4·(-40)·(-6)
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(31)-1}{2*-40}=\frac{-32}{-80}
=2/5
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(31)+1}{2*-40}=\frac{-30}{-80}
=3/8
$