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49x^2-1869x-3514=0
a = 49; b = -1869; c = -3514;
Δ = b2-4ac
Δ = -18692-4·49·(-3514)
Δ = 4181905
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{4181905}=\sqrt{8281*505}=\sqrt{8281}*\sqrt{505}=91\sqrt{505}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1869)-91\sqrt{505}}{2*49}=\frac{1869-91\sqrt{505}}{98} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1869)+91\sqrt{505}}{2*49}=\frac{1869+91\sqrt{505}}{98} $
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