31x-7x^2=12

Solution for 31x-7x^2=12 equation:

31x-7x^2=12

We move all terms to the left:

31x-7x^2-(12)=0

a = -7; b = 31; c = -12;
Δ = b2-4ac
Δ = 312-4·(-7)·(-12)
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(31)-25}{2*-7}=\frac{-56}{-14}
=+4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(31)+25}{2*-7}=\frac{-6}{-14}
=3/7
$