2c+3/c-5=10

Solution for 2c+3/c-5=10 equation:

2c+3/c-5=10

We move all terms to the left:

2c+3/c-5-(10)=0


Domain of the equation: c!=0

c∈R


We add all the numbers together, and all the variables

2c+3/c-15=0

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

Wy multiply elements

2c^2-15c+3=0

a = 2; b = -15; c = +3;
Δ = b2-4ac
Δ = -152-4·2·3
Δ = 201
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-\sqrt{201}}{2*2}=\frac{15-\sqrt{201}}{4}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+\sqrt{201}}{2*2}=\frac{15+\sqrt{201}}{4}
$