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2x^2-114x+216=0
a = 2; b = -114; c = +216;
Δ = b2-4ac
Δ = -1142-4·2·216
Δ = 11268
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{11268}=\sqrt{36*313}=\sqrt{36}*\sqrt{313}=6\sqrt{313}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-114)-6\sqrt{313}}{2*2}=\frac{114-6\sqrt{313}}{4} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-114)+6\sqrt{313}}{2*2}=\frac{114+6\sqrt{313}}{4} $
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