44x=x^2-135

Solution for 44x=x^2-135 equation:

44x=x^2-135

We move all terms to the left:

44x-(x^2-135)=0

We get rid of parentheses

-x^2+44x+135=0

We add all the numbers together, and all the variables

-1x^2+44x+135=0

a = -1; b = 44; c = +135;
Δ = b2-4ac
Δ = 442-4·(-1)·135
Δ = 2476
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:

$\sqrt{\Delta}=\sqrt{2476}=\sqrt{4*619}=\sqrt{4}*\sqrt{619}=2\sqrt{619}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(44)-2\sqrt{619}}{2*-1}=\frac{-44-2\sqrt{619}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(44)+2\sqrt{619}}{2*-1}=\frac{-44+2\sqrt{619}}{-2}
$