(8+c)(15/c+8)=15

Solution for (8+c)(15/c+8)=15 equation:

(8+c)(15/c+8)=15

We move all terms to the left:

(8+c)(15/c+8)-(15)=0


Domain of the equation: c+8)!=0

c∈R


We add all the numbers together, and all the variables

(c+8)(15/c+8)-15=0

We multiply parentheses ..

(+15c^2+8c+120c+64)-15=0

We get rid of parentheses

15c^2+8c+120c+64-15=0

We add all the numbers together, and all the variables

15c^2+128c+49=0

a = 15; b = 128; c = +49;
Δ = b2-4ac
Δ = 1282-4·15·49
Δ = 13444
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{13444}=\sqrt{4*3361}=\sqrt{4}*\sqrt{3361}=2\sqrt{3361}$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(128)-2\sqrt{3361}}{2*15}=\frac{-128-2\sqrt{3361}}{30}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(128)+2\sqrt{3361}}{2*15}=\frac{-128+2\sqrt{3361}}{30}
$