3/2c+23=38c=

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

3/2c+23=38c=

We move all terms to the left:

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


Domain of the equation: 2c!=0

c!=0/2

c!=0

c∈R


We add all the numbers together, and all the variables

-38c+3/2c+23=0

We multiply all the terms by the denominator


-38c*2c+23*2c+3=0

Wy multiply elements

-76c^2+46c+3=0

a = -76; b = 46; c = +3;
Δ = b2-4ac
Δ = 462-4·(-76)·3
Δ = 3028
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:

$\sqrt{\Delta}=\sqrt{3028}=\sqrt{4*757}=\sqrt{4}*\sqrt{757}=2\sqrt{757}$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(46)-2\sqrt{757}}{2*-76}=\frac{-46-2\sqrt{757}}{-152}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(46)+2\sqrt{757}}{2*-76}=\frac{-46+2\sqrt{757}}{-152}
$