c+1=4/c-2=7

Solution for c+1=4/c-2=7 equation:

c+1=4/c-2=7

We move all terms to the left:

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


Domain of the equation: c-2)!=0

c∈R


We get rid of parentheses

c-4/c+2+1=0

We multiply all the terms by the denominator


c*c+2*c+1*c-4=0

We add all the numbers together, and all the variables

3c+c*c-4=0

Wy multiply elements

c^2+3c-4=0

a = 1; b = 3; c = -4;
Δ = b2-4ac
Δ = 32-4·1·(-4)
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-5}{2*1}=\frac{-8}{2}
=-4
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+5}{2*1}=\frac{2}{2}
=1
$