45p^2+182p-168=0

Solution for 45p^2+182p-168=0 equation:

45p^2+182p-168=0

a = 45; b = 182; c = -168;
Δ = b2-4ac
Δ = 1822-4·45·(-168)
Δ = 63364
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:

$\sqrt{\Delta}=\sqrt{63364}=\sqrt{4*15841}=\sqrt{4}*\sqrt{15841}=2\sqrt{15841}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(182)-2\sqrt{15841}}{2*45}=\frac{-182-2\sqrt{15841}}{90}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(182)+2\sqrt{15841}}{2*45}=\frac{-182+2\sqrt{15841}}{90}
$