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50x^2-x-40=0
We add all the numbers together, and all the variables
50x^2-1x-40=0
a = 50; b = -1; c = -40;
Δ = b2-4ac
Δ = -12-4·50·(-40)
Δ = 8001
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{8001}=\sqrt{9*889}=\sqrt{9}*\sqrt{889}=3\sqrt{889}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-3\sqrt{889}}{2*50}=\frac{1-3\sqrt{889}}{100} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+3\sqrt{889}}{2*50}=\frac{1+3\sqrt{889}}{100} $
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