2(1.65)+c+1/2c=12.54

Solution for 2(1.65)+c+1/2c=12.54 equation:

2(1.65)+c+1/2c=12.54

We move all terms to the left:

2(1.65)+c+1/2c-(12.54)=0


Domain of the equation: 2c!=0

c!=0/2

c!=0

c∈R


We add all the numbers together, and all the variables

c+1/2c-9.24=0

We multiply all the terms by the denominator


c*2c-(9.24)*2c+1=0

We multiply parentheses

c*2c-18.48c+1=0

Wy multiply elements

2c^2-18.48c+1=0

a = 2; b = -18.48; c = +1;
Δ = b2-4ac
Δ = -18.482-4·2·1
Δ = 333.5104
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18.48)-\sqrt{333.5104}}{2*2}=\frac{18.48-\sqrt{333.5104}}{4}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18.48)+\sqrt{333.5104}}{2*2}=\frac{18.48+\sqrt{333.5104}}{4}
$