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X/5X-4+3X=12
We move all terms to the left:
X/5X-4+3X-(12)=0
Domain of the equation: 5X!=0We add all the numbers together, and all the variables
X!=0/5
X!=0
X∈R
3X+X/5X-16=0
We multiply all the terms by the denominator
3X*5X+X-16*5X=0
We add all the numbers together, and all the variables
X+3X*5X-16*5X=0
Wy multiply elements
15X^2+X-80X=0
We add all the numbers together, and all the variables
15X^2-79X=0
a = 15; b = -79; c = 0;
Δ = b2-4ac
Δ = -792-4·15·0
Δ = 6241
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{6241}=79$$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-79)-79}{2*15}=\frac{0}{30} =0 $$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-79)+79}{2*15}=\frac{158}{30} =5+4/15 $
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