1/4x+9=2x-8

Solution for 1/4x+9=2x-8 equation:

1/4x+9=2x-8

We move all terms to the left:

1/4x+9-(2x-8)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We get rid of parentheses

1/4x-2x+8+9=0

We multiply all the terms by the denominator


-2x*4x+8*4x+9*4x+1=0

Wy multiply elements

-8x^2+32x+36x+1=0

We add all the numbers together, and all the variables

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

a = -8; b = 68; c = +1;
Δ = b2-4ac
Δ = 682-4·(-8)·1
Δ = 4656
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:

$\sqrt{\Delta}=\sqrt{4656}=\sqrt{16*291}=\sqrt{16}*\sqrt{291}=4\sqrt{291}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(68)-4\sqrt{291}}{2*-8}=\frac{-68-4\sqrt{291}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(68)+4\sqrt{291}}{2*-8}=\frac{-68+4\sqrt{291}}{-16}
$