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1.5x+1/3x=-8.4
We move all terms to the left:
1.5x+1/3x-(-8.4)=0
Domain of the equation: 3x!=0We add all the numbers together, and all the variables
x!=0/3
x!=0
x∈R
1.5x+1/3x+8.4=0
We multiply all the terms by the denominator
(1.5x)*3x+(8.4)*3x+1=0
We add all the numbers together, and all the variables
(+1.5x)*3x+(8.4)*3x+1=0
We multiply parentheses
3x^2+25.2x+1=0
a = 3; b = 25.2; c = +1;
Δ = b2-4ac
Δ = 25.22-4·3·1
Δ = 623.04
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{-(25.2)-\sqrt{623.04}}{2*3}=\frac{-25.2-\sqrt{623.04}}{6} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25.2)+\sqrt{623.04}}{2*3}=\frac{-25.2+\sqrt{623.04}}{6} $
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