20/c=4c-7

Solution for 20/c=4c-7 equation:

20/c=4c-7

We move all terms to the left:

20/c-(4c-7)=0


Domain of the equation: c!=0

c∈R


We get rid of parentheses

20/c-4c+7=0

We multiply all the terms by the denominator


-4c*c+7*c+20=0

We add all the numbers together, and all the variables

7c-4c*c+20=0

Wy multiply elements

-4c^2+7c+20=0

a = -4; b = 7; c = +20;
Δ = b2-4ac
Δ = 72-4·(-4)·20
Δ = 369
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:

$\sqrt{\Delta}=\sqrt{369}=\sqrt{9*41}=\sqrt{9}*\sqrt{41}=3\sqrt{41}$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-3\sqrt{41}}{2*-4}=\frac{-7-3\sqrt{41}}{-8}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+3\sqrt{41}}{2*-4}=\frac{-7+3\sqrt{41}}{-8}
$