6p(2p-3)-11p=5

Solution for 6p(2p-3)-11p=5 equation:

6p(2p-3)-11p=5

We move all terms to the left:

6p(2p-3)-11p-(5)=0

We add all the numbers together, and all the variables

-11p+6p(2p-3)-5=0

We multiply parentheses

12p^2-11p-18p-5=0

We add all the numbers together, and all the variables

12p^2-29p-5=0

a = 12; b = -29; c = -5;
Δ = b2-4ac
Δ = -292-4·12·(-5)
Δ = 1081
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-29)-\sqrt{1081}}{2*12}=\frac{29-\sqrt{1081}}{24}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-29)+\sqrt{1081}}{2*12}=\frac{29+\sqrt{1081}}{24}
$