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-4x^2-27x-43=0
a = -4; b = -27; c = -43;
Δ = b2-4ac
Δ = -272-4·(-4)·(-43)
Δ = 41
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-\sqrt{41}}{2*-4}=\frac{27-\sqrt{41}}{-8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+\sqrt{41}}{2*-4}=\frac{27+\sqrt{41}}{-8} $
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