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

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

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

We move all terms to the left:

4x+(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

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

32x^2*2-520x*2+1=0

Wy multiply elements

64x^2-1040x+1=0

a = 64; b = -1040; c = +1;
Δ = b2-4ac
Δ = -10402-4·64·1
Δ = 1081344
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:

$\sqrt{\Delta}=\sqrt{1081344}=\sqrt{16384*66}=\sqrt{16384}*\sqrt{66}=128\sqrt{66}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1040)-128\sqrt{66}}{2*64}=\frac{1040-128\sqrt{66}}{128}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1040)+128\sqrt{66}}{2*64}=\frac{1040+128\sqrt{66}}{128}
$