3x+12/4x+11=0

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Solution for 3x+12/4x+11=0 equation: 



3x+12/4x+11=0



Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



We multiply all the terms by the denominator


3x*4x+11*4x+12=0

Wy multiply elements

12x^2+44x+12=0

a = 12; b = 44; c = +12;
Δ = b2-4ac
Δ = 442-4·12·12
Δ = 1360
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:


$\sqrt{\Delta}=\sqrt{1360}=\sqrt{16*85}=\sqrt{16}*\sqrt{85}=4\sqrt{85}$


$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(44)-4\sqrt{85}}{2*12}=\frac{-44-4\sqrt{85}}{24}
$


$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(44)+4\sqrt{85}}{2*12}=\frac{-44+4\sqrt{85}}{24}
$

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