2/3c-7c=-9

Solution for 2/3c-7c=-9 equation:

2/3c-7c=-9

We move all terms to the left:

2/3c-7c-(-9)=0


Domain of the equation: 3c!=0

c!=0/3

c!=0

c∈R


We add all the numbers together, and all the variables

-7c+2/3c+9=0

We multiply all the terms by the denominator


-7c*3c+9*3c+2=0

Wy multiply elements

-21c^2+27c+2=0

a = -21; b = 27; c = +2;
Δ = b2-4ac
Δ = 272-4·(-21)·2
Δ = 897
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{-(27)-\sqrt{897}}{2*-21}=\frac{-27-\sqrt{897}}{-42}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+\sqrt{897}}{2*-21}=\frac{-27+\sqrt{897}}{-42}
$