-c-7/2c=54

Solution for -c-7/2c=54 equation:

-c-7/2c=54

We move all terms to the left:

-c-7/2c-(54)=0


Domain of the equation: 2c!=0

c!=0/2

c!=0

c∈R


We add all the numbers together, and all the variables

-1c-7/2c-54=0

We multiply all the terms by the denominator


-1c*2c-54*2c-7=0

Wy multiply elements

-2c^2-108c-7=0

a = -2; b = -108; c = -7;
Δ = b2-4ac
Δ = -1082-4·(-2)·(-7)
Δ = 11608
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:

$\sqrt{\Delta}=\sqrt{11608}=\sqrt{4*2902}=\sqrt{4}*\sqrt{2902}=2\sqrt{2902}$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-108)-2\sqrt{2902}}{2*-2}=\frac{108-2\sqrt{2902}}{-4}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-108)+2\sqrt{2902}}{2*-2}=\frac{108+2\sqrt{2902}}{-4}
$