11x-6/4x+3=0

Solution for 11x-6/4x+3=0 equation:

11x-6/4x+3=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We multiply all the terms by the denominator


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}
$