3/2c+c+23=38

Solution for 3/2c+c+23=38 equation:

3/2c+c+23=38

We move all terms to the left:

3/2c+c+23-(38)=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+3/2c-15=0

We multiply all the terms by the denominator


c*2c-15*2c+3=0

Wy multiply elements

2c^2-30c+3=0

a = 2; b = -30; c = +3;
Δ = b2-4ac
Δ = -302-4·2·3
Δ = 876
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:

$\sqrt{\Delta}=\sqrt{876}=\sqrt{4*219}=\sqrt{4}*\sqrt{219}=2\sqrt{219}$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-2\sqrt{219}}{2*2}=\frac{30-2\sqrt{219}}{4}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+2\sqrt{219}}{2*2}=\frac{30+2\sqrt{219}}{4}
$