6p^2=9-20p

Solution for 6p^2=9-20p equation:

6p^2=9-20p

We move all terms to the left:

6p^2-(9-20p)=0

We add all the numbers together, and all the variables

6p^2-(-20p+9)=0

We get rid of parentheses

6p^2+20p-9=0

a = 6; b = 20; c = -9;
Δ = b2-4ac
Δ = 202-4·6·(-9)
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{-(20)-2\sqrt{154}}{2*6}=\frac{-20-2\sqrt{154}}{12}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+2\sqrt{154}}{2*6}=\frac{-20+2\sqrt{154}}{12}
$