55x=9x^2-324

Solution for 55x=9x^2-324 equation:

55x=9x^2-324

We move all terms to the left:

55x-(9x^2-324)=0

We get rid of parentheses

-9x^2+55x+324=0

a = -9; b = 55; c = +324;
Δ = b2-4ac
Δ = 552-4·(-9)·324
Δ = 14689
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{-(55)-\sqrt{14689}}{2*-9}=\frac{-55-\sqrt{14689}}{-18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(55)+\sqrt{14689}}{2*-9}=\frac{-55+\sqrt{14689}}{-18}
$