(1/7)(14-7p)-2=-2(1/2p+3)+6

Solution for (1/7)(14-7p)-2=-2(1/2p+3)+6 equation:

(1/7)(14-7p)-2=-2(1/2p+3)+6

We move all terms to the left:

(1/7)(14-7p)-2-(-2(1/2p+3)+6)=0


Domain of the equation: 7)(14-7p)!=0

p∈R



Domain of the equation: 2p+3)+6)!=0

p∈R


We add all the numbers together, and all the variables

(+1/7)(-7p+14)-(-2(1/2p+3)+6)-2=0

We multiply parentheses ..

(-7p^2+1/7*14)-(-2(1/2p+3)+6)-2=0

We calculate fractions


(-7p^2+2p+3)/196p^2+()/196p^2-2=0

We multiply all the terms by the denominator


(-7p^2+2p+3)-2*196p^2+()=0

We add all the numbers together, and all the variables

(-7p^2+2p+3)-2*196p^2=0

Wy multiply elements

(-7p^2+2p+3)-392p^2=0

We get rid of parentheses

-7p^2-392p^2+2p+3=0

We add all the numbers together, and all the variables

-399p^2+2p+3=0

a = -399; b = 2; c = +3;
Δ = b2-4ac
Δ = 22-4·(-399)·3
Δ = 4792
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:

$\sqrt{\Delta}=\sqrt{4792}=\sqrt{4*1198}=\sqrt{4}*\sqrt{1198}=2\sqrt{1198}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{1198}}{2*-399}=\frac{-2-2\sqrt{1198}}{-798}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{1198}}{2*-399}=\frac{-2+2\sqrt{1198}}{-798}
$