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5x^2-106x-480=0
a = 5; b = -106; c = -480;
Δ = b2-4ac
Δ = -1062-4·5·(-480)
Δ = 20836
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{20836}=\sqrt{4*5209}=\sqrt{4}*\sqrt{5209}=2\sqrt{5209}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-106)-2\sqrt{5209}}{2*5}=\frac{106-2\sqrt{5209}}{10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-106)+2\sqrt{5209}}{2*5}=\frac{106+2\sqrt{5209}}{10} $
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