c2=49/54

Solution for c2=49/54 equation:

c2=49/54

We move all terms to the left:

c2-(49/54)=0

We add all the numbers together, and all the variables

c2-(+49/54)=0

We add all the numbers together, and all the variables

c^2-(+49/54)=0

We get rid of parentheses

c^2-49/54=0

We multiply all the terms by the denominator


c^2*54-49=0

Wy multiply elements

54c^2-49=0

a = 54; b = 0; c = -49;
Δ = b2-4ac
Δ = 02-4·54·(-49)
Δ = 10584
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:

$\sqrt{\Delta}=\sqrt{10584}=\sqrt{1764*6}=\sqrt{1764}*\sqrt{6}=42\sqrt{6}$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-42\sqrt{6}}{2*54}=\frac{0-42\sqrt{6}}{108}
=-\frac{42\sqrt{6}}{108}
=-\frac{7\sqrt{6}}{18}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+42\sqrt{6}}{2*54}=\frac{0+42\sqrt{6}}{108}
=\frac{42\sqrt{6}}{108}
=\frac{7\sqrt{6}}{18}
$