5.7p-2/7p+12=6

Solution for 5.7p-2/7p+12=6 equation:

5.7p-2/7p+12=6

We move all terms to the left:

5.7p-2/7p+12-(6)=0


Domain of the equation: 7p!=0

p!=0/7

p!=0

p∈R


We add all the numbers together, and all the variables

5.7p-2/7p+6=0

We multiply all the terms by the denominator


(5.7p)*7p+6*7p-2=0

We add all the numbers together, and all the variables

(+5.7p)*7p+6*7p-2=0

We multiply parentheses

35p^2+6*7p-2=0

Wy multiply elements

35p^2+42p-2=0

a = 35; b = 42; c = -2;
Δ = b2-4ac
Δ = 422-4·35·(-2)
Δ = 2044
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:

$\sqrt{\Delta}=\sqrt{2044}=\sqrt{4*511}=\sqrt{4}*\sqrt{511}=2\sqrt{511}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(42)-2\sqrt{511}}{2*35}=\frac{-42-2\sqrt{511}}{70}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(42)+2\sqrt{511}}{2*35}=\frac{-42+2\sqrt{511}}{70}
$