1/4x+(x-7)=1+3x

Solution for 1/4x+(x-7)=1+3x equation:

1/4x+(x-7)=1+3x

We move all terms to the left:

1/4x+(x-7)-(1+3x)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

1/4x+(x-7)-(3x+1)=0

We get rid of parentheses

1/4x+x-3x-7-1=0

We multiply all the terms by the denominator


x*4x-3x*4x-7*4x-1*4x+1=0

Wy multiply elements

4x^2-12x^2-28x-4x+1=0

We add all the numbers together, and all the variables

-8x^2-32x+1=0

a = -8; b = -32; c = +1;
Δ = b2-4ac
Δ = -322-4·(-8)·1
Δ = 1056
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:

$\sqrt{\Delta}=\sqrt{1056}=\sqrt{16*66}=\sqrt{16}*\sqrt{66}=4\sqrt{66}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-4\sqrt{66}}{2*-8}=\frac{32-4\sqrt{66}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+4\sqrt{66}}{2*-8}=\frac{32+4\sqrt{66}}{-16}
$