Answer
$9x^2+25y^2-100+80x=0$
Work Step by Step
After multiplying with the denominator of the fraction: $r(5+4\cos{\theta})=10\\5r+4r\cos{\theta}=10\\5r=10-4r\cos{\theta}\\25r^2=(10-4r\cos{\theta})^2$. We know that $r^2=x^2+y^2$ and that $x=r\cos\theta,y=r\sin\theta$. Hence $25r^2=(10-4r\cos{\theta})^2$ becomes: $25(x^2+y^2)=(10-4x)^2\\25x^2+25y^2=100-80x+16x^2\\9x^2+25y^2-100+80x=0$
