1/4x-1+x=14

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

1/4x-1+x=14

We move all terms to the left:

1/4x-1+x-(14)=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-15=0

We multiply all the terms by the denominator


x*4x-15*4x+1=0

Wy multiply elements

4x^2-60x+1=0

a = 4; b = -60; c = +1;
Δ = b2-4ac
Δ = -602-4·4·1
Δ = 3584
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:

$\sqrt{\Delta}=\sqrt{3584}=\sqrt{256*14}=\sqrt{256}*\sqrt{14}=16\sqrt{14}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-16\sqrt{14}}{2*4}=\frac{60-16\sqrt{14}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+16\sqrt{14}}{2*4}=\frac{60+16\sqrt{14}}{8}
$