(-3/5)x-9=-27

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Solution for (-3/5)x-9=-27 equation:



(-3/5)x-9=-27
We move all terms to the left:
(-3/5)x-9-(-27)=0
Domain of the equation: 5)x!=0
x!=0/1
x!=0
x∈R
We add all the numbers together, and all the variables
(-3/5)x+18=0
We multiply parentheses
-3x^2+18=0
a = -3; b = 0; c = +18;
Δ = b2-4ac
Δ = 02-4·(-3)·18
Δ = 216
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:
$\sqrt{\Delta}=\sqrt{216}=\sqrt{36*6}=\sqrt{36}*\sqrt{6}=6\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{6}}{2*-3}=\frac{0-6\sqrt{6}}{-6} =-\frac{6\sqrt{6}}{-6} =-\frac{\sqrt{6}}{-1} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{6}}{2*-3}=\frac{0+6\sqrt{6}}{-6} =\frac{6\sqrt{6}}{-6} =\frac{\sqrt{6}}{-1} $

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