45p^2+120p-300=0

Solution for 45p^2+120p-300=0 equation:

45p^2+120p-300=0

a = 45; b = 120; c = -300;
Δ = b2-4ac
Δ = 1202-4·45·(-300)
Δ = 68400
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:

$\sqrt{\Delta}=\sqrt{68400}=\sqrt{3600*19}=\sqrt{3600}*\sqrt{19}=60\sqrt{19}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(120)-60\sqrt{19}}{2*45}=\frac{-120-60\sqrt{19}}{90}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(120)+60\sqrt{19}}{2*45}=\frac{-120+60\sqrt{19}}{90}
$