-1/4x+17=x-4

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

-1/4x+17=x-4

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

-4x^2+16x+68x-1=0

We add all the numbers together, and all the variables

-4x^2+84x-1=0

a = -4; b = 84; c = -1;
Δ = b2-4ac
Δ = 842-4·(-4)·(-1)
Δ = 7040
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:

$\sqrt{\Delta}=\sqrt{7040}=\sqrt{64*110}=\sqrt{64}*\sqrt{110}=8\sqrt{110}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(84)-8\sqrt{110}}{2*-4}=\frac{-84-8\sqrt{110}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(84)+8\sqrt{110}}{2*-4}=\frac{-84+8\sqrt{110}}{-8}
$