x+3x+1/4x=7225

Solution for x+3x+1/4x=7225 equation:

x+3x+1/4x=7225

We move all terms to the left:

x+3x+1/4x-(7225)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

4x+1/4x-7225=0

We multiply all the terms by the denominator


4x*4x-7225*4x+1=0

Wy multiply elements

16x^2-28900x+1=0

a = 16; b = -28900; c = +1;
Δ = b2-4ac
Δ = -289002-4·16·1
Δ = 835209936
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:

$\sqrt{\Delta}=\sqrt{835209936}=\sqrt{144*5800069}=\sqrt{144}*\sqrt{5800069}=12\sqrt{5800069}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28900)-12\sqrt{5800069}}{2*16}=\frac{28900-12\sqrt{5800069}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28900)+12\sqrt{5800069}}{2*16}=\frac{28900+12\sqrt{5800069}}{32}
$