7p-5+12p^2=-3p

Solution for 7p-5+12p^2=-3p equation:

7p-5+12p^2=-3p

We move all terms to the left:

7p-5+12p^2-(-3p)=0

We get rid of parentheses

12p^2+7p+3p-5=0

We add all the numbers together, and all the variables

12p^2+10p-5=0

a = 12; b = 10; c = -5;
Δ = b2-4ac
Δ = 102-4·12·(-5)
Δ = 340
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:

$\sqrt{\Delta}=\sqrt{340}=\sqrt{4*85}=\sqrt{4}*\sqrt{85}=2\sqrt{85}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{85}}{2*12}=\frac{-10-2\sqrt{85}}{24}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{85}}{2*12}=\frac{-10+2\sqrt{85}}{24}
$