8p^2=5-12p

Solution for 8p^2=5-12p equation:

8p^2=5-12p

We move all terms to the left:

8p^2-(5-12p)=0

We add all the numbers together, and all the variables

8p^2-(-12p+5)=0

We get rid of parentheses

8p^2+12p-5=0

a = 8; b = 12; c = -5;
Δ = b2-4ac
Δ = 122-4·8·(-5)
Δ = 304
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:

$\sqrt{\Delta}=\sqrt{304}=\sqrt{16*19}=\sqrt{16}*\sqrt{19}=4\sqrt{19}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-4\sqrt{19}}{2*8}=\frac{-12-4\sqrt{19}}{16}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+4\sqrt{19}}{2*8}=\frac{-12+4\sqrt{19}}{16}
$