7p^2=31p-12

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

7p^2=31p-12

We move all terms to the left:

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

We get rid of parentheses

7p^2-31p+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:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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