1/4x+1/4x+x+x=60

Solution for 1/4x+1/4x+x+x=60 equation:

1/4x+1/4x+x+x=60

We move all terms to the left:

1/4x+1/4x+x+x-(60)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

2x+1/4x+1/4x-60=0

We multiply all the terms by the denominator


2x*4x-60*4x+1+1=0

We add all the numbers together, and all the variables

2x*4x-60*4x+2=0

Wy multiply elements

8x^2-240x+2=0

a = 8; b = -240; c = +2;
Δ = b2-4ac
Δ = -2402-4·8·2
Δ = 57536
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:

$\sqrt{\Delta}=\sqrt{57536}=\sqrt{64*899}=\sqrt{64}*\sqrt{899}=8\sqrt{899}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-240)-8\sqrt{899}}{2*8}=\frac{240-8\sqrt{899}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-240)+8\sqrt{899}}{2*8}=\frac{240+8\sqrt{899}}{16}
$