5p^2-13p=84

Solution for 5p^2-13p=84 equation:

5p^2-13p=84

We move all terms to the left:

5p^2-13p-(84)=0

a = 5; b = -13; c = -84;
Δ = b2-4ac
Δ = -132-4·5·(-84)
Δ = 1849
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1849}=43$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-43}{2*5}=\frac{-30}{10}
=-3
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+43}{2*5}=\frac{56}{10}
=5+3/5
$