14p^2-23=4p^2+10p

Solution for 14p^2-23=4p^2+10p equation:

14p^2-23=4p^2+10p

We move all terms to the left:

14p^2-23-(4p^2+10p)=0

We get rid of parentheses

14p^2-4p^2-10p-23=0

We add all the numbers together, and all the variables

10p^2-10p-23=0

a = 10; b = -10; c = -23;
Δ = b2-4ac
Δ = -102-4·10·(-23)
Δ = 1020
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:

$\sqrt{\Delta}=\sqrt{1020}=\sqrt{4*255}=\sqrt{4}*\sqrt{255}=2\sqrt{255}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{255}}{2*10}=\frac{10-2\sqrt{255}}{20}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{255}}{2*10}=\frac{10+2\sqrt{255}}{20}
$