C(-3,5);y=5/9X+3

Solution for C(-3,5);y=5/9X+3 equation:

(-3.5)C=5/9C+3

We move all terms to the left:

(-3.5)C-(5/9C+3)=0


Domain of the equation: 9C+3)!=0

C∈R


We multiply parentheses

-3.5C-(5/9C+3)=0

We get rid of parentheses

-3.5C-5/9C-3=0

We multiply all the terms by the denominator


-(3.5C)*9C-3*9C-5=0

We add all the numbers together, and all the variables

-(+3.5C)*9C-3*9C-5=0

We multiply parentheses

-27C^2-3*9C-5=0

Wy multiply elements

-27C^2-27C-5=0

a = -27; b = -27; c = -5;
Δ = b2-4ac
Δ = -272-4·(-27)·(-5)
Δ = 189
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:

$\sqrt{\Delta}=\sqrt{189}=\sqrt{9*21}=\sqrt{9}*\sqrt{21}=3\sqrt{21}$
$C_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-3\sqrt{21}}{2*-27}=\frac{27-3\sqrt{21}}{-54}
$
$C_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+3\sqrt{21}}{2*-27}=\frac{27+3\sqrt{21}}{-54}
$