4p-5(p+6)p=3

Solution for 4p-5(p+6)p=3 equation:

4p-5(p+6)p=3

We move all terms to the left:

4p-5(p+6)p-(3)=0

We multiply parentheses

-5p^2+4p-30p-3=0

We add all the numbers together, and all the variables

-5p^2-26p-3=0

a = -5; b = -26; c = -3;
Δ = b2-4ac
Δ = -262-4·(-5)·(-3)
Δ = 616
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:

$\sqrt{\Delta}=\sqrt{616}=\sqrt{4*154}=\sqrt{4}*\sqrt{154}=2\sqrt{154}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-26)-2\sqrt{154}}{2*-5}=\frac{26-2\sqrt{154}}{-10}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-26)+2\sqrt{154}}{2*-5}=\frac{26+2\sqrt{154}}{-10}
$