5/7c=c+4

Solution for 5/7c=c+4 equation:

5/7c=c+4

We move all terms to the left:

5/7c-(c+4)=0


Domain of the equation: 7c!=0

c!=0/7

c!=0

c∈R


We get rid of parentheses

5/7c-c-4=0

We multiply all the terms by the denominator


-c*7c-4*7c+5=0

Wy multiply elements

-7c^2-28c+5=0

a = -7; b = -28; c = +5;
Δ = b2-4ac
Δ = -282-4·(-7)·5
Δ = 924
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:

$\sqrt{\Delta}=\sqrt{924}=\sqrt{4*231}=\sqrt{4}*\sqrt{231}=2\sqrt{231}$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-2\sqrt{231}}{2*-7}=\frac{28-2\sqrt{231}}{-14}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+2\sqrt{231}}{2*-7}=\frac{28+2\sqrt{231}}{-14}
$