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2x^2-117x+324=0
a = 2; b = -117; c = +324;
Δ = b2-4ac
Δ = -1172-4·2·324
Δ = 11097
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{11097}=\sqrt{81*137}=\sqrt{81}*\sqrt{137}=9\sqrt{137}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-117)-9\sqrt{137}}{2*2}=\frac{117-9\sqrt{137}}{4} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-117)+9\sqrt{137}}{2*2}=\frac{117+9\sqrt{137}}{4} $
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