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5x^2-14x-216=0
a = 5; b = -14; c = -216;
Δ = b2-4ac
Δ = -142-4·5·(-216)
Δ = 4516
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{4516}=\sqrt{4*1129}=\sqrt{4}*\sqrt{1129}=2\sqrt{1129}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{1129}}{2*5}=\frac{14-2\sqrt{1129}}{10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{1129}}{2*5}=\frac{14+2\sqrt{1129}}{10} $
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