x+2x+(x+2)+1/4*2x=65

Solution for x+2x+(x+2)+1/4*2x=65 equation:

x+2x+(x+2)+1/4*2x=65

We move all terms to the left:

x+2x+(x+2)+1/4*2x-(65)=0


Domain of the equation: 4*2x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

3x+(x+2)+1/4*2x-65=0

We get rid of parentheses

3x+x+1/4*2x+2-65=0

We multiply all the terms by the denominator


3x*4*2x+x*4*2x+2*4*2x-65*4*2x+1=0

Wy multiply elements

24x^2*2+8x^2*2+16x*2-520x*2+1=0

Wy multiply elements

48x^2+16x^2+32x-1040x+1=0

We add all the numbers together, and all the variables

64x^2-1008x+1=0

a = 64; b = -1008; c = +1;
Δ = b2-4ac
Δ = -10082-4·64·1
Δ = 1015808
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:

$\sqrt{\Delta}=\sqrt{1015808}=\sqrt{16384*62}=\sqrt{16384}*\sqrt{62}=128\sqrt{62}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1008)-128\sqrt{62}}{2*64}=\frac{1008-128\sqrt{62}}{128}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1008)+128\sqrt{62}}{2*64}=\frac{1008+128\sqrt{62}}{128}
$