X(2+5y)=9

Solution for X(2+5y)=9 equation:

X(2+5X)=9

We move all terms to the left:

X(2+5X)-(9)=0

We add all the numbers together, and all the variables

X(5X+2)-9=0

We multiply parentheses

5X^2+2X-9=0

a = 5; b = 2; c = -9;
Δ = b2-4ac
Δ = 22-4·5·(-9)
Δ = 184
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:

$\sqrt{\Delta}=\sqrt{184}=\sqrt{4*46}=\sqrt{4}*\sqrt{46}=2\sqrt{46}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{46}}{2*5}=\frac{-2-2\sqrt{46}}{10}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{46}}{2*5}=\frac{-2+2\sqrt{46}}{10}
$