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37x^2+222x-96=0
a = 37; b = 222; c = -96;
Δ = b2-4ac
Δ = 2222-4·37·(-96)
Δ = 63492
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{63492}=\sqrt{4*15873}=\sqrt{4}*\sqrt{15873}=2\sqrt{15873}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(222)-2\sqrt{15873}}{2*37}=\frac{-222-2\sqrt{15873}}{74} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(222)+2\sqrt{15873}}{2*37}=\frac{-222+2\sqrt{15873}}{74} $
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