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9.5+2/3x=-x+20
We move all terms to the left:
9.5+2/3x-(-x+20)=0
Domain of the equation: 3x!=0We add all the numbers together, and all the variables
x!=0/3
x!=0
x∈R
2/3x-(-1x+20)+9.5=0
We get rid of parentheses
2/3x+1x-20+9.5=0
We multiply all the terms by the denominator
1x*3x-20*3x+(9.5)*3x+2=0
We multiply parentheses
1x*3x-20*3x+28.5x+2=0
Wy multiply elements
3x^2-60x+28.5x+2=0
We add all the numbers together, and all the variables
3x^2-31.5x+2=0
a = 3; b = -31.5; c = +2;
Δ = b2-4ac
Δ = -31.52-4·3·2
Δ = 968.25
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{-(-31.5)-\sqrt{968.25}}{2*3}=\frac{31.5-\sqrt{968.25}}{6} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-31.5)+\sqrt{968.25}}{2*3}=\frac{31.5+\sqrt{968.25}}{6} $
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