11/4x+27=3x

Solution for 11/4x+27=3x equation:

11/4x+27=3x

We move all terms to the left:

11/4x+27-(3x)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

-3x+11/4x+27=0

We multiply all the terms by the denominator


-3x*4x+27*4x+11=0

Wy multiply elements

-12x^2+108x+11=0

a = -12; b = 108; c = +11;
Δ = b2-4ac
Δ = 1082-4·(-12)·11
Δ = 12192
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:

$\sqrt{\Delta}=\sqrt{12192}=\sqrt{16*762}=\sqrt{16}*\sqrt{762}=4\sqrt{762}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(108)-4\sqrt{762}}{2*-12}=\frac{-108-4\sqrt{762}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(108)+4\sqrt{762}}{2*-12}=\frac{-108+4\sqrt{762}}{-24}
$