3p^2-18p=9p-56

Solution for 3p^2-18p=9p-56 equation:

3p^2-18p=9p-56

We move all terms to the left:

3p^2-18p-(9p-56)=0

We get rid of parentheses

3p^2-18p-9p+56=0

We add all the numbers together, and all the variables

3p^2-27p+56=0

a = 3; b = -27; c = +56;
Δ = b2-4ac
Δ = -272-4·3·56
Δ = 57
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{-(-27)-\sqrt{57}}{2*3}=\frac{27-\sqrt{57}}{6}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+\sqrt{57}}{2*3}=\frac{27+\sqrt{57}}{6}
$