3x-4=1/2x+9

Solution for 3x-4=1/2x+9 equation:

3x-4=1/2x+9

We move all terms to the left:

3x-4-(1/2x+9)=0


Domain of the equation: 2x+9)!=0

x∈R


We get rid of parentheses

3x-1/2x-9-4=0

We multiply all the terms by the denominator


3x*2x-9*2x-4*2x-1=0

Wy multiply elements

6x^2-18x-8x-1=0

We add all the numbers together, and all the variables

6x^2-26x-1=0

a = 6; b = -26; c = -1;
Δ = b2-4ac
Δ = -262-4·6·(-1)
Δ = 700
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:

$\sqrt{\Delta}=\sqrt{700}=\sqrt{100*7}=\sqrt{100}*\sqrt{7}=10\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-26)-10\sqrt{7}}{2*6}=\frac{26-10\sqrt{7}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-26)+10\sqrt{7}}{2*6}=\frac{26+10\sqrt{7}}{12}
$