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4x^2-120x+404=0
a = 4; b = -120; c = +404;
Δ = b2-4ac
Δ = -1202-4·4·404
Δ = 7936
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{7936}=\sqrt{256*31}=\sqrt{256}*\sqrt{31}=16\sqrt{31}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-120)-16\sqrt{31}}{2*4}=\frac{120-16\sqrt{31}}{8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-120)+16\sqrt{31}}{2*4}=\frac{120+16\sqrt{31}}{8} $
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