3/4x-1/4x+14=3,x=

Solution for 3/4x-1/4x+14=3,x= equation:

3/4x-1/4x+14=3.x=

We move all terms to the left:

3/4x-1/4x+14-(3.x)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

3/4x-1/4x-(+3.x)+14=0

We get rid of parentheses

3/4x-1/4x-3.x+14=0

We multiply all the terms by the denominator


-(3.x)*4x+14*4x+3-1=0

We add all the numbers together, and all the variables

-(+3.x)*4x+14*4x+3-1=0

We add all the numbers together, and all the variables

-(+3.x)*4x+14*4x+2=0

We multiply parentheses

-12x^2+14*4x+2=0

Wy multiply elements

-12x^2+56x+2=0

a = -12; b = 56; c = +2;
Δ = b2-4ac
Δ = 562-4·(-12)·2
Δ = 3232
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:

$\sqrt{\Delta}=\sqrt{3232}=\sqrt{16*202}=\sqrt{16}*\sqrt{202}=4\sqrt{202}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(56)-4\sqrt{202}}{2*-12}=\frac{-56-4\sqrt{202}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(56)+4\sqrt{202}}{2*-12}=\frac{-56+4\sqrt{202}}{-24}
$