12p^2=35+16p

Solution for 12p^2=35+16p equation:

12p^2=35+16p

We move all terms to the left:

12p^2-(35+16p)=0

We add all the numbers together, and all the variables

12p^2-(16p+35)=0

We get rid of parentheses

12p^2-16p-35=0

a = 12; b = -16; c = -35;
Δ = b2-4ac
Δ = -162-4·12·(-35)
Δ = 1936
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1936}=44$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-44}{2*12}=\frac{-28}{24}
=-1+1/6
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+44}{2*12}=\frac{60}{24}
=2+1/2
$