-3/2p=10-p

Solution for -3/2p=10-p equation:

-3/2p=10-p

We move all terms to the left:

-3/2p-(10-p)=0


Domain of the equation: 2p!=0

p!=0/2

p!=0

p∈R


We add all the numbers together, and all the variables

-3/2p-(-1p+10)=0

We get rid of parentheses

-3/2p+1p-10=0

We multiply all the terms by the denominator


1p*2p-10*2p-3=0

Wy multiply elements

2p^2-20p-3=0

a = 2; b = -20; c = -3;
Δ = b2-4ac
Δ = -202-4·2·(-3)
Δ = 424
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:

$\sqrt{\Delta}=\sqrt{424}=\sqrt{4*106}=\sqrt{4}*\sqrt{106}=2\sqrt{106}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-2\sqrt{106}}{2*2}=\frac{20-2\sqrt{106}}{4}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+2\sqrt{106}}{2*2}=\frac{20+2\sqrt{106}}{4}
$