1/4x+2=x-5

Solution for 1/4x+2=x-5 equation:

1/4x+2=x-5

We move all terms to the left:

1/4x+2-(x-5)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We get rid of parentheses

1/4x-x+5+2=0

We multiply all the terms by the denominator


-x*4x+5*4x+2*4x+1=0

Wy multiply elements

-4x^2+20x+8x+1=0

We add all the numbers together, and all the variables

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

a = -4; b = 28; c = +1;
Δ = b2-4ac
Δ = 282-4·(-4)·1
Δ = 800
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:

$\sqrt{\Delta}=\sqrt{800}=\sqrt{400*2}=\sqrt{400}*\sqrt{2}=20\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-20\sqrt{2}}{2*-4}=\frac{-28-20\sqrt{2}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+20\sqrt{2}}{2*-4}=\frac{-28+20\sqrt{2}}{-8}
$