10+5c=45/5c

Solution for 10+5c=45/5c equation:

10+5c=45/5c

We move all terms to the left:

10+5c-(45/5c)=0


Domain of the equation: 5c)!=0

c!=0/1

c!=0

c∈R


We add all the numbers together, and all the variables

5c-(+45/5c)+10=0

We get rid of parentheses

5c-45/5c+10=0

We multiply all the terms by the denominator


5c*5c+10*5c-45=0

Wy multiply elements

25c^2+50c-45=0

a = 25; b = 50; c = -45;
Δ = b2-4ac
Δ = 502-4·25·(-45)
Δ = 7000
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:

$\sqrt{\Delta}=\sqrt{7000}=\sqrt{100*70}=\sqrt{100}*\sqrt{70}=10\sqrt{70}$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(50)-10\sqrt{70}}{2*25}=\frac{-50-10\sqrt{70}}{50}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(50)+10\sqrt{70}}{2*25}=\frac{-50+10\sqrt{70}}{50}
$