9/5(c)+32c=30

Solution for 9/5(c)+32c=30 equation:

9/5(c)+32c=30

We move all terms to the left:

9/5(c)+32c-(30)=0


Domain of the equation: 5c!=0

c!=0/5

c!=0

c∈R


We add all the numbers together, and all the variables

32c+9/5c-30=0

We multiply all the terms by the denominator


32c*5c-30*5c+9=0

Wy multiply elements

160c^2-150c+9=0

a = 160; b = -150; c = +9;
Δ = b2-4ac
Δ = -1502-4·160·9
Δ = 16740
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:

$\sqrt{\Delta}=\sqrt{16740}=\sqrt{36*465}=\sqrt{36}*\sqrt{465}=6\sqrt{465}$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-150)-6\sqrt{465}}{2*160}=\frac{150-6\sqrt{465}}{320}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-150)+6\sqrt{465}}{2*160}=\frac{150+6\sqrt{465}}{320}
$