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42x^2+5x-2=0
a = 42; b = 5; c = -2;
Δ = b2-4ac
Δ = 52-4·42·(-2)
Δ = 361
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{361}=19$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-19}{2*42}=\frac{-24}{84} =-2/7 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+19}{2*42}=\frac{14}{84} =1/6 $
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