7c-10=32/c

Solution for 7c-10=32/c equation:

7c-10=32/c

We move all terms to the left:

7c-10-(32/c)=0


Domain of the equation: c)!=0

c!=0/1

c!=0

c∈R


We add all the numbers together, and all the variables

7c-(+32/c)-10=0

We get rid of parentheses

7c-32/c-10=0

We multiply all the terms by the denominator


7c*c-10*c-32=0

We add all the numbers together, and all the variables

-10c+7c*c-32=0

Wy multiply elements

7c^2-10c-32=0

a = 7; b = -10; c = -32;
Δ = b2-4ac
Δ = -102-4·7·(-32)
Δ = 996
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:

$\sqrt{\Delta}=\sqrt{996}=\sqrt{4*249}=\sqrt{4}*\sqrt{249}=2\sqrt{249}$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{249}}{2*7}=\frac{10-2\sqrt{249}}{14}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{249}}{2*7}=\frac{10+2\sqrt{249}}{14}
$