1/4x+x=-3=1/2x

Solution for 1/4x+x=-3=1/2x equation:

1/4x+x=-3=1/2x

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

x+1/4x+3=0

We multiply all the terms by the denominator


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

Wy multiply elements

4x^2+12x+1=0

a = 4; b = 12; c = +1;
Δ = b2-4ac
Δ = 122-4·4·1
Δ = 128
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:

$\sqrt{\Delta}=\sqrt{128}=\sqrt{64*2}=\sqrt{64}*\sqrt{2}=8\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-8\sqrt{2}}{2*4}=\frac{-12-8\sqrt{2}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+8\sqrt{2}}{2*4}=\frac{-12+8\sqrt{2}}{8}
$