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6x-18/5x+11=0
Domain of the equation: 5x!=0We multiply all the terms by the denominator
x!=0/5
x!=0
x∈R
6x*5x+11*5x-18=0
Wy multiply elements
30x^2+55x-18=0
a = 30; b = 55; c = -18;
Δ = b2-4ac
Δ = 552-4·30·(-18)
Δ = 5185
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{-(55)-\sqrt{5185}}{2*30}=\frac{-55-\sqrt{5185}}{60} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(55)+\sqrt{5185}}{2*30}=\frac{-55+\sqrt{5185}}{60} $
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