(6p^2-p-8)-(-4p^2+2p-3)=0

Solution for (6p^2-p-8)-(-4p^2+2p-3)=0 equation:

(6p^2-p-8)-(-4p^2+2p-3)=0

We get rid of parentheses

4p^2+6p^2-2p-p+3-8=0

We add all the numbers together, and all the variables

10p^2-3p-5=0

a = 10; b = -3; c = -5;
Δ = b2-4ac
Δ = -32-4·10·(-5)
Δ = 209
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{-(-3)-\sqrt{209}}{2*10}=\frac{3-\sqrt{209}}{20}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{209}}{2*10}=\frac{3+\sqrt{209}}{20}
$