x+297=18x^2-44

Solution for x+297=18x^2-44 equation:

x+297=18x^2-44

We move all terms to the left:

x+297-(18x^2-44)=0

We get rid of parentheses

-18x^2+x+44+297=0

We add all the numbers together, and all the variables

-18x^2+x+341=0

a = -18; b = 1; c = +341;
Δ = b2-4ac
Δ = 12-4·(-18)·341
Δ = 24553
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{24553}}{2*-18}=\frac{-1-\sqrt{24553}}{-36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{24553}}{2*-18}=\frac{-1+\sqrt{24553}}{-36}
$