1/4x+4=2x-17

Solution for 1/4x+4=2x-17 equation:

1/4x+4=2x-17

We move all terms to the left:

1/4x+4-(2x-17)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We get rid of parentheses

1/4x-2x+17+4=0

We multiply all the terms by the denominator


-2x*4x+17*4x+4*4x+1=0

Wy multiply elements

-8x^2+68x+16x+1=0

We add all the numbers together, and all the variables

-8x^2+84x+1=0

a = -8; b = 84; c = +1;
Δ = b2-4ac
Δ = 842-4·(-8)·1
Δ = 7088
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:

$\sqrt{\Delta}=\sqrt{7088}=\sqrt{16*443}=\sqrt{16}*\sqrt{443}=4\sqrt{443}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(84)-4\sqrt{443}}{2*-8}=\frac{-84-4\sqrt{443}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(84)+4\sqrt{443}}{2*-8}=\frac{-84+4\sqrt{443}}{-16}
$