/6x+3x-6=75

Solution for /6x+3x-6=75 equation:

/6x+3x-6=75

We move all terms to the left:

/6x+3x-6-(75)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We add all the numbers together, and all the variables

3x+/6x-81=0

We multiply all the terms by the denominator


3x*6x-81*6x+=0

We add all the numbers together, and all the variables

3x*6x-81*6x=0

Wy multiply elements

18x^2-486x=0

a = 18; b = -486; c = 0;
Δ = b2-4ac
Δ = -4862-4·18·0
Δ = 236196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{236196}=486$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-486)-486}{2*18}=\frac{0}{36}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-486)+486}{2*18}=\frac{972}{36}
=27
$