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3x-40/3x+30=14.50
We move all terms to the left:
3x-40/3x+30-(14.50)=0
Domain of the equation: 3x!=0We add all the numbers together, and all the variables
x!=0/3
x!=0
x∈R
3x-40/3x+30-(14.5)=0
We add all the numbers together, and all the variables
3x-40/3x+15.5=0
We multiply all the terms by the denominator
3x*3x+(15.5)*3x-40=0
We multiply parentheses
3x*3x+46.5x-40=0
Wy multiply elements
9x^2+46.5x-40=0
a = 9; b = 46.5; c = -40;
Δ = b2-4ac
Δ = 46.52-4·9·(-40)
Δ = 3602.25
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{-(46.5)-\sqrt{3602.25}}{2*9}=\frac{-46.5-\sqrt{3602.25}}{18} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(46.5)+\sqrt{3602.25}}{2*9}=\frac{-46.5+\sqrt{3602.25}}{18} $
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