2/4x-1=x+7

Solution for 2/4x-1=x+7 equation:

2/4x-1=x+7

We move all terms to the left:

2/4x-1-(x+7)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We get rid of parentheses

2/4x-x-7-1=0

We multiply all the terms by the denominator


-x*4x-7*4x-1*4x+2=0

Wy multiply elements

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

We add all the numbers together, and all the variables

-4x^2-32x+2=0

a = -4; b = -32; c = +2;
Δ = b2-4ac
Δ = -322-4·(-4)·2
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*-4}=\frac{32-4\sqrt{66}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+4\sqrt{66}}{2*-4}=\frac{32+4\sqrt{66}}{-8}
$