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8x^2+46x+11=0
a = 8; b = 46; c = +11;
Δ = b2-4ac
Δ = 462-4·8·11
Δ = 1764
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{1764}=42$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(46)-42}{2*8}=\frac{-88}{16} =-5+1/2 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(46)+42}{2*8}=\frac{-4}{16} =-1/4 $
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