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37x^2+48x-5=0
a = 37; b = 48; c = -5;
Δ = b2-4ac
Δ = 482-4·37·(-5)
Δ = 3044
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{3044}=\sqrt{4*761}=\sqrt{4}*\sqrt{761}=2\sqrt{761}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-2\sqrt{761}}{2*37}=\frac{-48-2\sqrt{761}}{74} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+2\sqrt{761}}{2*37}=\frac{-48+2\sqrt{761}}{74} $
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