x^2-45x^2=-324

Solution for x^2-45x^2=-324 equation:

x^2-45x^2=-324

We move all terms to the left:

x^2-45x^2-(-324)=0

We add all the numbers together, and all the variables

-44x^2+324=0

a = -44; b = 0; c = +324;
Δ = b2-4ac
Δ = 02-4·(-44)·324
Δ = 57024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{57024}=\sqrt{5184*11}=\sqrt{5184}*\sqrt{11}=72\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-72\sqrt{11}}{2*-44}=\frac{0-72\sqrt{11}}{-88}
=-\frac{72\sqrt{11}}{-88}
=-\frac{9\sqrt{11}}{-11}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+72\sqrt{11}}{2*-44}=\frac{0+72\sqrt{11}}{-88}
=\frac{72\sqrt{11}}{-88}
=\frac{9\sqrt{11}}{-11}
$