3/5p-14=p+13

Solution for 3/5p-14=p+13 equation:

3/5p-14=p+13

We move all terms to the left:

3/5p-14-(p+13)=0


Domain of the equation: 5p!=0

p!=0/5

p!=0

p∈R


We get rid of parentheses

3/5p-p-13-14=0

We multiply all the terms by the denominator


-p*5p-13*5p-14*5p+3=0

Wy multiply elements

-5p^2-65p-70p+3=0

We add all the numbers together, and all the variables

-5p^2-135p+3=0

a = -5; b = -135; c = +3;
Δ = b2-4ac
Δ = -1352-4·(-5)·3
Δ = 18285
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{-(-135)-\sqrt{18285}}{2*-5}=\frac{135-\sqrt{18285}}{-10}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-135)+\sqrt{18285}}{2*-5}=\frac{135+\sqrt{18285}}{-10}
$