c=1/4c-10

Solution for c=1/4c-10 equation:

c=1/4c-10

We move all terms to the left:

c-(1/4c-10)=0


Domain of the equation: 4c-10)!=0

c∈R


We get rid of parentheses

c-1/4c+10=0

We multiply all the terms by the denominator


c*4c+10*4c-1=0

Wy multiply elements

4c^2+40c-1=0

a = 4; b = 40; c = -1;
Δ = b2-4ac
Δ = 402-4·4·(-1)
Δ = 1616
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:

$\sqrt{\Delta}=\sqrt{1616}=\sqrt{16*101}=\sqrt{16}*\sqrt{101}=4\sqrt{101}$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-4\sqrt{101}}{2*4}=\frac{-40-4\sqrt{101}}{8}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+4\sqrt{101}}{2*4}=\frac{-40+4\sqrt{101}}{8}
$