2x-9=1/4x+5

Solution for 2x-9=1/4x+5 equation:

2x-9=1/4x+5

We move all terms to the left:

2x-9-(1/4x+5)=0


Domain of the equation: 4x+5)!=0

x∈R


We get rid of parentheses

2x-1/4x-5-9=0

We multiply all the terms by the denominator


2x*4x-5*4x-9*4x-1=0

Wy multiply elements

8x^2-20x-36x-1=0

We add all the numbers together, and all the variables

8x^2-56x-1=0

a = 8; b = -56; c = -1;
Δ = b2-4ac
Δ = -562-4·8·(-1)
Δ = 3168
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:

$\sqrt{\Delta}=\sqrt{3168}=\sqrt{144*22}=\sqrt{144}*\sqrt{22}=12\sqrt{22}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-56)-12\sqrt{22}}{2*8}=\frac{56-12\sqrt{22}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-56)+12\sqrt{22}}{2*8}=\frac{56+12\sqrt{22}}{16}
$