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2+150L^2=1813500
We move all terms to the left:
2+150L^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} $
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