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x+3x-6+2/3x+2=150
We move all terms to the left:
x+3x-6+2/3x+2-(150)=0
Domain of the equation: 3x!=0We add all the numbers together, and all the variables
x!=0/3
x!=0
x∈R
4x+2/3x-154=0
We multiply all the terms by the denominator
4x*3x-154*3x+2=0
Wy multiply elements
12x^2-462x+2=0
a = 12; b = -462; c = +2;
Δ = b2-4ac
Δ = -4622-4·12·2
Δ = 213348
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{213348}=\sqrt{4*53337}=\sqrt{4}*\sqrt{53337}=2\sqrt{53337}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-462)-2\sqrt{53337}}{2*12}=\frac{462-2\sqrt{53337}}{24} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-462)+2\sqrt{53337}}{2*12}=\frac{462+2\sqrt{53337}}{24} $
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