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

Solution for (5p^2-3)+(2p^2-3p)=0 equation:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

7p^2-3p-3=0

a = 7; b = -3; c = -3;
Δ = b2-4ac
Δ = -32-4·7·(-3)
Δ = 93
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{93}}{2*7}=\frac{3-\sqrt{93}}{14}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{93}}{2*7}=\frac{3+\sqrt{93}}{14}
$