-2p^2+13p+78=4p+10

Solution for -2p^2+13p+78=4p+10 equation:

-2p^2+13p+78=4p+10

We move all terms to the left:

-2p^2+13p+78-(4p+10)=0

We get rid of parentheses

-2p^2+13p-4p-10+78=0

We add all the numbers together, and all the variables

-2p^2+9p+68=0

a = -2; b = 9; c = +68;
Δ = b2-4ac
Δ = 92-4·(-2)·68
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-25}{2*-2}=\frac{-34}{-4}
=8+1/2
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+25}{2*-2}=\frac{16}{-4}
=-4
$