20c+18/9c+3c=75

Solution for 20c+18/9c+3c=75 equation:

20c+18/9c+3c=75

We move all terms to the left:

20c+18/9c+3c-(75)=0


Domain of the equation: 9c!=0

c!=0/9

c!=0

c∈R


We add all the numbers together, and all the variables

23c+18/9c-75=0

We multiply all the terms by the denominator


23c*9c-75*9c+18=0

Wy multiply elements

207c^2-675c+18=0

a = 207; b = -675; c = +18;
Δ = b2-4ac
Δ = -6752-4·207·18
Δ = 440721
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:

$\sqrt{\Delta}=\sqrt{440721}=\sqrt{81*5441}=\sqrt{81}*\sqrt{5441}=9\sqrt{5441}$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-675)-9\sqrt{5441}}{2*207}=\frac{675-9\sqrt{5441}}{414}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-675)+9\sqrt{5441}}{2*207}=\frac{675+9\sqrt{5441}}{414}
$