4p+4/2p-6=10

Solution for 4p+4/2p-6=10 equation:

4p+4/2p-6=10

We move all terms to the left:

4p+4/2p-6-(10)=0


Domain of the equation: 2p!=0

p!=0/2

p!=0

p∈R


We add all the numbers together, and all the variables

4p+4/2p-16=0

We multiply all the terms by the denominator


4p*2p-16*2p+4=0

Wy multiply elements

8p^2-32p+4=0

a = 8; b = -32; c = +4;
Δ = b2-4ac
Δ = -322-4·8·4
Δ = 896
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:

$\sqrt{\Delta}=\sqrt{896}=\sqrt{64*14}=\sqrt{64}*\sqrt{14}=8\sqrt{14}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-8\sqrt{14}}{2*8}=\frac{32-8\sqrt{14}}{16}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+8\sqrt{14}}{2*8}=\frac{32+8\sqrt{14}}{16}
$