9p^2=-42p-24

Solution for 9p^2=-42p-24 equation:

9p^2=-42p-24

We move all terms to the left:

9p^2-(-42p-24)=0

We get rid of parentheses

9p^2+42p+24=0

a = 9; b = 42; c = +24;
Δ = b2-4ac
Δ = 422-4·9·24
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(42)-30}{2*9}=\frac{-72}{18}
=-4
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(42)+30}{2*9}=\frac{-12}{18}
=-2/3
$