12p^2=16+7p

Solution for 12p^2=16+7p equation:

12p^2=16+7p

We move all terms to the left:

12p^2-(16+7p)=0

We add all the numbers together, and all the variables

12p^2-(7p+16)=0

We get rid of parentheses

12p^2-7p-16=0

a = 12; b = -7; c = -16;
Δ = b2-4ac
Δ = -72-4·12·(-16)
Δ = 817
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-\sqrt{817}}{2*12}=\frac{7-\sqrt{817}}{24}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{817}}{2*12}=\frac{7+\sqrt{817}}{24}
$