7p^2=5+6p

Solution for 7p^2=5+6p equation:

7p^2=5+6p

We move all terms to the left:

7p^2-(5+6p)=0

We add all the numbers together, and all the variables

7p^2-(6p+5)=0

We get rid of parentheses

7p^2-6p-5=0

a = 7; b = -6; c = -5;
Δ = b2-4ac
Δ = -62-4·7·(-5)
Δ = 176
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:

$\sqrt{\Delta}=\sqrt{176}=\sqrt{16*11}=\sqrt{16}*\sqrt{11}=4\sqrt{11}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-4\sqrt{11}}{2*7}=\frac{6-4\sqrt{11}}{14}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+4\sqrt{11}}{2*7}=\frac{6+4\sqrt{11}}{14}
$