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2/3x-15+x=180
We move all terms to the left:
2/3x-15+x-(180)=0
Domain of the equation: 3x!=0We add all the numbers together, and all the variables
x!=0/3
x!=0
x∈R
x+2/3x-195=0
We multiply all the terms by the denominator
x*3x-195*3x+2=0
Wy multiply elements
3x^2-585x+2=0
a = 3; b = -585; c = +2;
Δ = b2-4ac
Δ = -5852-4·3·2
Δ = 342201
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-585)-\sqrt{342201}}{2*3}=\frac{585-\sqrt{342201}}{6} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-585)+\sqrt{342201}}{2*3}=\frac{585+\sqrt{342201}}{6} $
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