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2/3x+1.3x-4.6=2.2
We move all terms to the left:
2/3x+1.3x-4.6-(2.2)=0
Domain of the equation: 3x!=0We add all the numbers together, and all the variables
x!=0/3
x!=0
x∈R
1.3x+2/3x-6.8=0
We multiply all the terms by the denominator
(1.3x)*3x-(6.8)*3x+2=0
We add all the numbers together, and all the variables
(+1.3x)*3x-(6.8)*3x+2=0
We multiply parentheses
3x^2-20.4x+2=0
a = 3; b = -20.4; c = +2;
Δ = b2-4ac
Δ = -20.42-4·3·2
Δ = 392.16
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{-(-20.4)-\sqrt{392.16}}{2*3}=\frac{20.4-\sqrt{392.16}}{6} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20.4)+\sqrt{392.16}}{2*3}=\frac{20.4+\sqrt{392.16}}{6} $
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