18x2=x+3

Solution for 18x2=x+3 equation:

18x^2=x+3

We move all terms to the left:

18x^2-(x+3)=0

We get rid of parentheses

18x^2-x-3=0

We add all the numbers together, and all the variables

18x^2-1x-3=0

a = 18; b = -1; c = -3;
Δ = b2-4ac
Δ = -12-4·18·(-3)
Δ = 217
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-\sqrt{217}}{2*18}=\frac{1-\sqrt{217}}{36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{217}}{2*18}=\frac{1+\sqrt{217}}{36}
$