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4x^2+83x+408=0
a = 4; b = 83; c = +408;
Δ = b2-4ac
Δ = 832-4·4·408
Δ = 361
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{361}=19$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(83)-19}{2*4}=\frac{-102}{8} =-12+3/4 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(83)+19}{2*4}=\frac{-64}{8} =-8 $
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