1/2c+3/5=-1-3/4c

Solution for 1/2c+3/5=-1-3/4c equation:

1/2c+3/5=-1-3/4c

We move all terms to the left:

1/2c+3/5-(-1-3/4c)=0


Domain of the equation: 2c!=0

c!=0/2

c!=0

c∈R



Domain of the equation: 4c)!=0

c!=0/1

c!=0

c∈R


We add all the numbers together, and all the variables

1/2c-(-3/4c-1)+3/5=0

We get rid of parentheses

1/2c+3/4c+1+3/5=0

We calculate fractions


96c^2/200c^2+100c/200c^2+150c/200c^2+1=0

We multiply all the terms by the denominator


96c^2+100c+150c+1*200c^2=0

We add all the numbers together, and all the variables

96c^2+250c+1*200c^2=0

Wy multiply elements

96c^2+200c^2+250c=0

We add all the numbers together, and all the variables

296c^2+250c=0

a = 296; b = 250; c = 0;
Δ = b2-4ac
Δ = 2502-4·296·0
Δ = 62500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{62500}=250$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(250)-250}{2*296}=\frac{-500}{592}
=-125/148
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(250)+250}{2*296}=\frac{0}{592}
=0
$