7p^2+4p=5p^2+8p+5

Solution for 7p^2+4p=5p^2+8p+5 equation:

7p^2+4p=5p^2+8p+5

We move all terms to the left:

7p^2+4p-(5p^2+8p+5)=0

We get rid of parentheses

7p^2-5p^2+4p-8p-5=0

We add all the numbers together, and all the variables

2p^2-4p-5=0

a = 2; b = -4; c = -5;
Δ = b2-4ac
Δ = -42-4·2·(-5)
Δ = 56
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:

$\sqrt{\Delta}=\sqrt{56}=\sqrt{4*14}=\sqrt{4}*\sqrt{14}=2\sqrt{14}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{14}}{2*2}=\frac{4-2\sqrt{14}}{4}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{14}}{2*2}=\frac{4+2\sqrt{14}}{4}
$