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4x-(16/x-3)=0
Domain of the equation: x-3)!=0We get rid of parentheses
x∈R
4x-16/x+3=0
We multiply all the terms by the denominator
4x*x+3*x-16=0
We add all the numbers together, and all the variables
3x+4x*x-16=0
Wy multiply elements
4x^2+3x-16=0
a = 4; b = 3; c = -16;
Δ = b2-4ac
Δ = 32-4·4·(-16)
Δ = 265
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{-(3)-\sqrt{265}}{2*4}=\frac{-3-\sqrt{265}}{8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{265}}{2*4}=\frac{-3+\sqrt{265}}{8} $
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