3p^2-11p+5=-3

Solution for 3p^2-11p+5=-3 equation:

3p^2-11p+5=-3

We move all terms to the left:

3p^2-11p+5-(-3)=0

We add all the numbers together, and all the variables

3p^2-11p+8=0

a = 3; b = -11; c = +8;
Δ = b2-4ac
Δ = -112-4·3·8
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-5}{2*3}=\frac{6}{6}
=1
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+5}{2*3}=\frac{16}{6}
=2+2/3
$