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46x^2-112x-49=0
a = 46; b = -112; c = -49;
Δ = b2-4ac
Δ = -1122-4·46·(-49)
Δ = 21560
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{21560}=\sqrt{196*110}=\sqrt{196}*\sqrt{110}=14\sqrt{110}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-112)-14\sqrt{110}}{2*46}=\frac{112-14\sqrt{110}}{92} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-112)+14\sqrt{110}}{2*46}=\frac{112+14\sqrt{110}}{92} $
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