1/4c-4=-5c+59

Solution for 1/4c-4=-5c+59 equation:

1/4c-4=-5c+59

We move all terms to the left:

1/4c-4-(-5c+59)=0


Domain of the equation: 4c!=0

c!=0/4

c!=0

c∈R


We get rid of parentheses

1/4c+5c-59-4=0

We multiply all the terms by the denominator


5c*4c-59*4c-4*4c+1=0

Wy multiply elements

20c^2-236c-16c+1=0

We add all the numbers together, and all the variables

20c^2-252c+1=0

a = 20; b = -252; c = +1;
Δ = b2-4ac
Δ = -2522-4·20·1
Δ = 63424
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:

$\sqrt{\Delta}=\sqrt{63424}=\sqrt{64*991}=\sqrt{64}*\sqrt{991}=8\sqrt{991}$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-252)-8\sqrt{991}}{2*20}=\frac{252-8\sqrt{991}}{40}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-252)+8\sqrt{991}}{2*20}=\frac{252+8\sqrt{991}}{40}
$