P=-3x2+30x-45

Solution for P=-3x2+30x-45 equation:

=-3P^2+30P-45

We move all terms to the left:

-(-3P^2+30P-45)=0

We get rid of parentheses

3P^2-30P+45=0

a = 3; b = -30; c = +45;
Δ = b2-4ac
Δ = -302-4·3·45
Δ = 360
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{360}=\sqrt{36*10}=\sqrt{36}*\sqrt{10}=6\sqrt{10}$
$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-6\sqrt{10}}{2*3}=\frac{30-6\sqrt{10}}{6}
$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+6\sqrt{10}}{2*3}=\frac{30+6\sqrt{10}}{6}
$