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45x^2+44x-1=0
a = 45; b = 44; c = -1;
Δ = b2-4ac
Δ = 442-4·45·(-1)
Δ = 2116
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{2116}=46$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(44)-46}{2*45}=\frac{-90}{90} =-1 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(44)+46}{2*45}=\frac{2}{90} =1/45 $
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