X(9x+1)=4x^2-8x+18

Solution for X(9x+1)=4x^2-8x+18 equation:

X(9X+1)=4X^2-8X+18

We move all terms to the left:

X(9X+1)-(4X^2-8X+18)=0

We multiply parentheses

9X^2+X-(4X^2-8X+18)=0

We get rid of parentheses

9X^2-4X^2+X+8X-18=0

We add all the numbers together, and all the variables

5X^2+9X-18=0

a = 5; b = 9; c = -18;
Δ = b2-4ac
Δ = 92-4·5·(-18)
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-21}{2*5}=\frac{-30}{10}
=-3
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+21}{2*5}=\frac{12}{10}
=1+1/5
$