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4.61x^2+43.4x-5421=0
a = 4.61; b = 43.4; c = -5421;
Δ = b2-4ac
Δ = 43.42-4·4.61·(-5421)
Δ = 101846.8
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{-(43.4)-\sqrt{101846.8}}{2*4.61}=\frac{-43.4-\sqrt{101846.8}}{9.22} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(43.4)+\sqrt{101846.8}}{2*4.61}=\frac{-43.4+\sqrt{101846.8}}{9.22} $
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