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5x+6/3x-9=2.33
We move all terms to the left:
5x+6/3x-9-(2.33)=0
Domain of the equation: 3x!=0We add all the numbers together, and all the variables
x!=0/3
x!=0
x∈R
5x+6/3x-11.33=0
We multiply all the terms by the denominator
5x*3x-(11.33)*3x+6=0
We multiply parentheses
5x*3x-33.99x+6=0
Wy multiply elements
15x^2-33.99x+6=0
a = 15; b = -33.99; c = +6;
Δ = b2-4ac
Δ = -33.992-4·15·6
Δ = 795.3201
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{-(-33.99)-\sqrt{795.3201}}{2*15}=\frac{33.99-\sqrt{795.3201}}{30} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-33.99)+\sqrt{795.3201}}{2*15}=\frac{33.99+\sqrt{795.3201}}{30} $
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