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42x^2+6x-115=0
a = 42; b = 6; c = -115;
Δ = b2-4ac
Δ = 62-4·42·(-115)
Δ = 19356
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{19356}=\sqrt{4*4839}=\sqrt{4}*\sqrt{4839}=2\sqrt{4839}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{4839}}{2*42}=\frac{-6-2\sqrt{4839}}{84} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{4839}}{2*42}=\frac{-6+2\sqrt{4839}}{84} $
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