c-5/11c=42

Solution for c-5/11c=42 equation:

c-5/11c=42

We move all terms to the left:

c-5/11c-(42)=0


Domain of the equation: 11c!=0

c!=0/11

c!=0

c∈R


We multiply all the terms by the denominator


c*11c-42*11c-5=0

Wy multiply elements

11c^2-462c-5=0

a = 11; b = -462; c = -5;
Δ = b2-4ac
Δ = -4622-4·11·(-5)
Δ = 213664
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:

$\sqrt{\Delta}=\sqrt{213664}=\sqrt{16*13354}=\sqrt{16}*\sqrt{13354}=4\sqrt{13354}$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-462)-4\sqrt{13354}}{2*11}=\frac{462-4\sqrt{13354}}{22}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-462)+4\sqrt{13354}}{2*11}=\frac{462+4\sqrt{13354}}{22}
$