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7.5x+2/3x=8.5
We move all terms to the left:
7.5x+2/3x-(8.5)=0
Domain of the equation: 3x!=0We add all the numbers together, and all the variables
x!=0/3
x!=0
x∈R
7.5x+2/3x-8.5=0
We multiply all the terms by the denominator
(7.5x)*3x-(8.5)*3x+2=0
We add all the numbers together, and all the variables
(+7.5x)*3x-(8.5)*3x+2=0
We multiply parentheses
21x^2-25.5x+2=0
a = 21; b = -25.5; c = +2;
Δ = b2-4ac
Δ = -25.52-4·21·2
Δ = 482.25
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{-(-25.5)-\sqrt{482.25}}{2*21}=\frac{25.5-\sqrt{482.25}}{42} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25.5)+\sqrt{482.25}}{2*21}=\frac{25.5+\sqrt{482.25}}{42} $
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