(2p+3)-(5p+7)/6p+11=-10/23

Solution for (2p+3)-(5p+7)/6p+11=-10/23 equation:

(2p+3)-(5p+7)/6p+11=-10/23

We move all terms to the left:

(2p+3)-(5p+7)/6p+11-(-10/23)=0


Domain of the equation: 6p!=0

p!=0/6

p!=0

p∈R


We get rid of parentheses

2p-(5p+7)/6p+3+11+10/23=0

We calculate fractions


2p+(-115p-161)/138p+60p/138p+3+11=0

We add all the numbers together, and all the variables

2p+(-115p-161)/138p+60p/138p+14=0

We multiply all the terms by the denominator


2p*138p+(-115p-161)+60p+14*138p=0

We add all the numbers together, and all the variables

60p+2p*138p+(-115p-161)+14*138p=0

Wy multiply elements

276p^2+60p+(-115p-161)+1932p=0

We get rid of parentheses

276p^2+60p-115p+1932p-161=0

We add all the numbers together, and all the variables

276p^2+1877p-161=0

a = 276; b = 1877; c = -161;
Δ = b2-4ac
Δ = 18772-4·276·(-161)
Δ = 3700873
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1877)-\sqrt{3700873}}{2*276}=\frac{-1877-\sqrt{3700873}}{552}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1877)+\sqrt{3700873}}{2*276}=\frac{-1877+\sqrt{3700873}}{552}
$