4p^2=-14p-6

Solution for 4p^2=-14p-6 equation:

4p^2=-14p-6

We move all terms to the left:

4p^2-(-14p-6)=0

We get rid of parentheses

4p^2+14p+6=0

a = 4; b = 14; c = +6;
Δ = b2-4ac
Δ = 142-4·4·6
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-10}{2*4}=\frac{-24}{8}
=-3
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+10}{2*4}=\frac{-4}{8}
=-1/2
$