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4/x-2=9-7x
We move all terms to the left:
4/x-2-(9-7x)=0
Domain of the equation: x!=0We add all the numbers together, and all the variables
x∈R
4/x-(-7x+9)-2=0
We get rid of parentheses
4/x+7x-9-2=0
We multiply all the terms by the denominator
7x*x-9*x-2*x+4=0
We add all the numbers together, and all the variables
-11x+7x*x+4=0
Wy multiply elements
7x^2-11x+4=0
a = 7; b = -11; c = +4;
Δ = b2-4ac
Δ = -112-4·7·4
Δ = 9
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{9}=3$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-3}{2*7}=\frac{8}{14} =4/7 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+3}{2*7}=\frac{14}{14} =1 $
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