1/2p+5=-9p

Solution for 1/2p+5=-9p equation:

1/2p+5=-9p

We move all terms to the left:

1/2p+5-(-9p)=0


Domain of the equation: 2p!=0

p!=0/2

p!=0

p∈R


We get rid of parentheses

1/2p+9p+5=0

We multiply all the terms by the denominator


9p*2p+5*2p+1=0

Wy multiply elements

18p^2+10p+1=0

a = 18; b = 10; c = +1;
Δ = b2-4ac
Δ = 102-4·18·1
Δ = 28
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{28}=\sqrt{4*7}=\sqrt{4}*\sqrt{7}=2\sqrt{7}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{7}}{2*18}=\frac{-10-2\sqrt{7}}{36}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{7}}{2*18}=\frac{-10+2\sqrt{7}}{36}
$