1/4x+4=3;x=-4

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

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

We move all terms to the left:

1/4x+4-(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+1/4x+4=0

We multiply all the terms by the denominator


-3x*4x+4*4x+1=0

Wy multiply elements

-12x^2+16x+1=0

a = -12; b = 16; c = +1;
Δ = b2-4ac
Δ = 162-4·(-12)·1
Δ = 304
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:

$\sqrt{\Delta}=\sqrt{304}=\sqrt{16*19}=\sqrt{16}*\sqrt{19}=4\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-4\sqrt{19}}{2*-12}=\frac{-16-4\sqrt{19}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+4\sqrt{19}}{2*-12}=\frac{-16+4\sqrt{19}}{-24}
$