(5/2)c=81/3

Solution for (5/2)c=81/3 equation:

(5/2)c=81/3

We move all terms to the left:

(5/2)c-(81/3)=0


Domain of the equation: 2)c!=0

c!=0/1

c!=0

c∈R


We add all the numbers together, and all the variables

(+5/2)c-27=0

We multiply parentheses

5c^2-27=0

a = 5; b = 0; c = -27;
Δ = b2-4ac
Δ = 02-4·5·(-27)
Δ = 540
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:

$\sqrt{\Delta}=\sqrt{540}=\sqrt{36*15}=\sqrt{36}*\sqrt{15}=6\sqrt{15}$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{15}}{2*5}=\frac{0-6\sqrt{15}}{10}
=-\frac{6\sqrt{15}}{10}
=-\frac{3\sqrt{15}}{5}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{15}}{2*5}=\frac{0+6\sqrt{15}}{10}
=\frac{6\sqrt{15}}{10}
=\frac{3\sqrt{15}}{5}
$