1813500=2L+150x2

Solution for 1813500=2L+150x2 equation:

1813500=2+150L^2

We move all terms to the left:

1813500-(2+150L^2)=0

We get rid of parentheses

-150L^2-2+1813500=0

We add all the numbers together, and all the variables

-150L^2+1813498=0

a = -150; b = 0; c = +1813498;
Δ = b2-4ac
Δ = 02-4·(-150)·1813498
Δ = 1088098800
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:

$\sqrt{\Delta}=\sqrt{1088098800}=\sqrt{400*2720247}=\sqrt{400}*\sqrt{2720247}=20\sqrt{2720247}$
$L_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-20\sqrt{2720247}}{2*-150}=\frac{0-20\sqrt{2720247}}{-300}
=-\frac{20\sqrt{2720247}}{-300}
=-\frac{\sqrt{2720247}}{-15}
$
$L_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+20\sqrt{2720247}}{2*-150}=\frac{0+20\sqrt{2720247}}{-300}
=\frac{20\sqrt{2720247}}{-300}
=\frac{\sqrt{2720247}}{-15}
$