7p^2=-58p-16

Solution for 7p^2=-58p-16 equation:

7p^2=-58p-16

We move all terms to the left:

7p^2-(-58p-16)=0

We get rid of parentheses

7p^2+58p+16=0

a = 7; b = 58; c = +16;
Δ = b2-4ac
Δ = 582-4·7·16
Δ = 2916
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2916}=54$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(58)-54}{2*7}=\frac{-112}{14}
=-8
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(58)+54}{2*7}=\frac{-4}{14}
=-2/7
$