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10x^2+3500x-66000-150000=0
We add all the numbers together, and all the variables
10x^2+3500x-216000=0
a = 10; b = 3500; c = -216000;
Δ = b2-4ac
Δ = 35002-4·10·(-216000)
Δ = 20890000
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{20890000}=\sqrt{10000*2089}=\sqrt{10000}*\sqrt{2089}=100\sqrt{2089}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3500)-100\sqrt{2089}}{2*10}=\frac{-3500-100\sqrt{2089}}{20} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3500)+100\sqrt{2089}}{2*10}=\frac{-3500+100\sqrt{2089}}{20} $
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