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X/3X-5+2X=25-5X
We move all terms to the left:
X/3X-5+2X-(25-5X)=0
Domain of the equation: 3X!=0We add all the numbers together, and all the variables
X!=0/3
X!=0
X∈R
X/3X+2X-(-5X+25)-5=0
We add all the numbers together, and all the variables
2X+X/3X-(-5X+25)-5=0
We get rid of parentheses
2X+X/3X+5X-25-5=0
We multiply all the terms by the denominator
2X*3X+X+5X*3X-25*3X-5*3X=0
We add all the numbers together, and all the variables
X+2X*3X+5X*3X-25*3X-5*3X=0
Wy multiply elements
6X^2+15X^2+X-75X-15X=0
We add all the numbers together, and all the variables
21X^2-89X=0
a = 21; b = -89; c = 0;
Δ = b2-4ac
Δ = -892-4·21·0
Δ = 7921
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}$$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{7921}=89$$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-89)-89}{2*21}=\frac{0}{42} =0 $$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-89)+89}{2*21}=\frac{178}{42} =4+5/21 $
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