1/2c=14c=24

Solution for 1/2c=14c=24 equation:

1/2c=14c=24

We move all terms to the left:

1/2c-(14c)=0


Domain of the equation: 2c!=0

c!=0/2

c!=0

c∈R


We add all the numbers together, and all the variables

-14c+1/2c=0

We multiply all the terms by the denominator


-14c*2c+1=0

Wy multiply elements

-28c^2+1=0

a = -28; b = 0; c = +1;
Δ = b2-4ac
Δ = 02-4·(-28)·1
Δ = 112
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:

$\sqrt{\Delta}=\sqrt{112}=\sqrt{16*7}=\sqrt{16}*\sqrt{7}=4\sqrt{7}$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{7}}{2*-28}=\frac{0-4\sqrt{7}}{-56}
=-\frac{4\sqrt{7}}{-56}
=-\frac{\sqrt{7}}{-14}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{7}}{2*-28}=\frac{0+4\sqrt{7}}{-56}
=\frac{4\sqrt{7}}{-56}
=\frac{\sqrt{7}}{-14}
$