5+9x^2=18x

Solution for 5+9x^2=18x equation:

5+9x^2=18x

We move all terms to the left:

5+9x^2-(18x)=0

a = 9; b = -18; c = +5;
Δ = b2-4ac
Δ = -182-4·9·5
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-12}{2*9}=\frac{6}{18}
=1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+12}{2*9}=\frac{30}{18}
=1+2/3
$