3x-9/1x-4=6

Solution for 3x-9/1x-4=6 equation:

3x-9/1x-4=6

We move all terms to the left:

3x-9/1x-4-(6)=0


Domain of the equation: 1x!=0

x∈R


We add all the numbers together, and all the variables

3x-9/1x-10=0

We multiply all the terms by the denominator


3x*1x-10*1x-9=0

Wy multiply elements

3x^2-10x-9=0

a = 3; b = -10; c = -9;
Δ = b2-4ac
Δ = -102-4·3·(-9)
Δ = 208
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:

$\sqrt{\Delta}=\sqrt{208}=\sqrt{16*13}=\sqrt{16}*\sqrt{13}=4\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-4\sqrt{13}}{2*3}=\frac{10-4\sqrt{13}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+4\sqrt{13}}{2*3}=\frac{10+4\sqrt{13}}{6}
$