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35x^2-5000x-150000=0
a = 35; b = -5000; c = -150000;
Δ = b2-4ac
Δ = -50002-4·35·(-150000)
Δ = 46000000
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{46000000}=\sqrt{1000000*46}=\sqrt{1000000}*\sqrt{46}=1000\sqrt{46}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5000)-1000\sqrt{46}}{2*35}=\frac{5000-1000\sqrt{46}}{70} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5000)+1000\sqrt{46}}{2*35}=\frac{5000+1000\sqrt{46}}{70} $
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