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11x-6/4x+3=0
Domain of the equation: 4x!=0We multiply all the terms by the denominator
x!=0/4
x!=0
x∈R
11x*4x+3*4x-6=0
Wy multiply elements
44x^2+12x-6=0
a = 44; b = 12; c = -6;
Δ = b2-4ac
Δ = 122-4·44·(-6)
Δ = 1200
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1200}=\sqrt{400*3}=\sqrt{400}*\sqrt{3}=20\sqrt{3}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-20\sqrt{3}}{2*44}=\frac{-12-20\sqrt{3}}{88} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+20\sqrt{3}}{2*44}=\frac{-12+20\sqrt{3}}{88} $
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