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4x^2+133x-65.4375=0
a = 4; b = 133; c = -65.4375;
Δ = b2-4ac
Δ = 1332-4·4·(-65.4375)
Δ = 18736
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{18736}=\sqrt{16*1171}=\sqrt{16}*\sqrt{1171}=4\sqrt{1171}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(133)-4\sqrt{1171}}{2*4}=\frac{-133-4\sqrt{1171}}{8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(133)+4\sqrt{1171}}{2*4}=\frac{-133+4\sqrt{1171}}{8} $
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