Given a linear equation pass through the point(6,4) and two axes, and formed a triangle...

Given a linear equation pass through the point(6,4) and two axes, and formed a triangle with area 6. I want to find the equation of that line.
My attempt is letting the equation be ${\displaystyle \frac{y-4}{x-6}=m}$. Then using the fact that the area of triangle is 6, forming the equation ${\displaystyle \frac{1}{2}\text{base}\star \text{height}=6}$. I got the base and height of the triangle from the axes, ${\displaystyle \text{base}=6-\frac{4}{m}}$ and ${\displaystyle \text{height}=4-6m}$
Then substitute the equation ${\displaystyle \frac{1}{2}\text{base}\star \text{height}=6}$ and get ${\displaystyle 36m^2-36m+16=0}$ which leads to no solution. Can anyone let me know what's wrong?