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-2/3x+5=20-x
We move all terms to the left:
-2/3x+5-(20-x)=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)+5=0
We get rid of parentheses
-2/3x+1x-20+5=0
We multiply all the terms by the denominator
1x*3x-20*3x+5*3x-2=0
Wy multiply elements
3x^2-60x+15x-2=0
We add all the numbers together, and all the variables
3x^2-45x-2=0
a = 3; b = -45; c = -2;
Δ = b2-4ac
Δ = -452-4·3·(-2)
Δ = 2049
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{-(-45)-\sqrt{2049}}{2*3}=\frac{45-\sqrt{2049}}{6} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+\sqrt{2049}}{2*3}=\frac{45+\sqrt{2049}}{6} $
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