7p+6=5/6p-62

Solution for 7p+6=5/6p-62 equation:

7p+6=5/6p-62

We move all terms to the left:

7p+6-(5/6p-62)=0


Domain of the equation: 6p-62)!=0

p∈R


We get rid of parentheses

7p-5/6p+62+6=0

We multiply all the terms by the denominator


7p*6p+62*6p+6*6p-5=0

Wy multiply elements

42p^2+372p+36p-5=0

We add all the numbers together, and all the variables

42p^2+408p-5=0

a = 42; b = 408; c = -5;
Δ = b2-4ac
Δ = 4082-4·42·(-5)
Δ = 167304
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:

$\sqrt{\Delta}=\sqrt{167304}=\sqrt{4*41826}=\sqrt{4}*\sqrt{41826}=2\sqrt{41826}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(408)-2\sqrt{41826}}{2*42}=\frac{-408-2\sqrt{41826}}{84}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(408)+2\sqrt{41826}}{2*42}=\frac{-408+2\sqrt{41826}}{84}
$