l*l-45=9000

Solution for l*l-45=9000 equation:

l*l-45=9000

We move all terms to the left:

l*l-45-(9000)=0

We add all the numbers together, and all the variables

l*l-9045=0

Wy multiply elements

l^2-9045=0

a = 1; b = 0; c = -9045;
Δ = b2-4ac
Δ = 02-4·1·(-9045)
Δ = 36180
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$l_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$l_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{36180}=\sqrt{36*1005}=\sqrt{36}*\sqrt{1005}=6\sqrt{1005}$
$l_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{1005}}{2*1}=\frac{0-6\sqrt{1005}}{2}
=-\frac{6\sqrt{1005}}{2}
=-3\sqrt{1005}
$
$l_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{1005}}{2*1}=\frac{0+6\sqrt{1005}}{2}
=\frac{6\sqrt{1005}}{2}
=3\sqrt{1005}
$