(41.5+c)(10c+1)=c

Solution for (41.5+c)(10c+1)=c equation:

(41.5+c)(10c+1)=c

We move all terms to the left:

(41.5+c)(10c+1)-(c)=0

We add all the numbers together, and all the variables

(c+41.5)(10c+1)-c=0

We add all the numbers together, and all the variables

-1c+(c+41.5)(10c+1)=0

We multiply parentheses ..

(+10c^2+c+415c+41.5)-1c=0

We get rid of parentheses

10c^2+c+415c-1c+41.5=0

We add all the numbers together, and all the variables

10c^2+415c+41.5=0

a = 10; b = 415; c = +41.5;
Δ = b2-4ac
Δ = 4152-4·10·41.5
Δ = 170565
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(415)-\sqrt{170565}}{2*10}=\frac{-415-\sqrt{170565}}{20}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(415)+\sqrt{170565}}{2*10}=\frac{-415+\sqrt{170565}}{20}
$