1/4x+17=x-40

Solution for 1/4x+17=x-40 equation:

1/4x+17=x-40

We move all terms to the left:

1/4x+17-(x-40)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We get rid of parentheses

1/4x-x+40+17=0

We multiply all the terms by the denominator


-x*4x+40*4x+17*4x+1=0

Wy multiply elements

-4x^2+160x+68x+1=0

We add all the numbers together, and all the variables

-4x^2+228x+1=0

a = -4; b = 228; c = +1;
Δ = b2-4ac
Δ = 2282-4·(-4)·1
Δ = 52000
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:

$\sqrt{\Delta}=\sqrt{52000}=\sqrt{400*130}=\sqrt{400}*\sqrt{130}=20\sqrt{130}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(228)-20\sqrt{130}}{2*-4}=\frac{-228-20\sqrt{130}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(228)+20\sqrt{130}}{2*-4}=\frac{-228+20\sqrt{130}}{-8}
$