2x-9=3/4x+9

Solution for 2x-9=3/4x+9 equation:

2x-9=3/4x+9

We move all terms to the left:

2x-9-(3/4x+9)=0


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

x∈R


We get rid of parentheses

2x-3/4x-9-9=0

We multiply all the terms by the denominator


2x*4x-9*4x-9*4x-3=0

Wy multiply elements

8x^2-36x-36x-3=0

We add all the numbers together, and all the variables

8x^2-72x-3=0

a = 8; b = -72; c = -3;
Δ = b2-4ac
Δ = -722-4·8·(-3)
Δ = 5280
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:

$\sqrt{\Delta}=\sqrt{5280}=\sqrt{16*330}=\sqrt{16}*\sqrt{330}=4\sqrt{330}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-72)-4\sqrt{330}}{2*8}=\frac{72-4\sqrt{330}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-72)+4\sqrt{330}}{2*8}=\frac{72+4\sqrt{330}}{16}
$