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8x^2+44x-24=0
a = 8; b = 44; c = -24;
Δ = b2-4ac
Δ = 442-4·8·(-24)
Δ = 2704
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{2704}=52$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(44)-52}{2*8}=\frac{-96}{16} =-6 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(44)+52}{2*8}=\frac{8}{16} =1/2 $
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