-5p^2+9p=-38

Solution for -5p^2+9p=-38 equation:

-5p^2+9p=-38

We move all terms to the left:

-5p^2+9p-(-38)=0

We add all the numbers together, and all the variables

-5p^2+9p+38=0

a = -5; b = 9; c = +38;
Δ = b2-4ac
Δ = 92-4·(-5)·38
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-29}{2*-5}=\frac{-38}{-10}
=3+4/5
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+29}{2*-5}=\frac{20}{-10}
=-2
$