2x+7=1/4x+9

Solution for 2x+7=1/4x+9 equation:

2x+7=1/4x+9

We move all terms to the left:

2x+7-(1/4x+9)=0


Domain of the equation: 4x+9)!=0

x∈R


We get rid of parentheses

2x-1/4x-9+7=0

We multiply all the terms by the denominator


2x*4x-9*4x+7*4x-1=0

Wy multiply elements

8x^2-36x+28x-1=0

We add all the numbers together, and all the variables

8x^2-8x-1=0

a = 8; b = -8; c = -1;
Δ = b2-4ac
Δ = -82-4·8·(-1)
Δ = 96
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:

$\sqrt{\Delta}=\sqrt{96}=\sqrt{16*6}=\sqrt{16}*\sqrt{6}=4\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{6}}{2*8}=\frac{8-4\sqrt{6}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{6}}{2*8}=\frac{8+4\sqrt{6}}{16}
$