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5x^2-24x-142=0
a = 5; b = -24; c = -142;
Δ = b2-4ac
Δ = -242-4·5·(-142)
Δ = 3416
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{3416}=\sqrt{4*854}=\sqrt{4}*\sqrt{854}=2\sqrt{854}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-2\sqrt{854}}{2*5}=\frac{24-2\sqrt{854}}{10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+2\sqrt{854}}{2*5}=\frac{24+2\sqrt{854}}{10} $
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