5p^2-11p=78

Solution for 5p^2-11p=78 equation:

5p^2-11p=78

We move all terms to the left:

5p^2-11p-(78)=0

a = 5; b = -11; c = -78;
Δ = b2-4ac
Δ = -112-4·5·(-78)
Δ = 1681
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1681}=41$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-41}{2*5}=\frac{-30}{10}
=-3
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+41}{2*5}=\frac{52}{10}
=5+1/5
$