1/4x+x=130

Solution for 1/4x+x=130 equation:

1/4x+x=130

We move all terms to the left:

1/4x+x-(130)=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-130=0

We multiply all the terms by the denominator


x*4x-130*4x+1=0

Wy multiply elements

4x^2-520x+1=0

a = 4; b = -520; c = +1;
Δ = b2-4ac
Δ = -5202-4·4·1
Δ = 270384
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:

$\sqrt{\Delta}=\sqrt{270384}=\sqrt{16*16899}=\sqrt{16}*\sqrt{16899}=4\sqrt{16899}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-520)-4\sqrt{16899}}{2*4}=\frac{520-4\sqrt{16899}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-520)+4\sqrt{16899}}{2*4}=\frac{520+4\sqrt{16899}}{8}
$