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4x^2-108x+81=0
a = 4; b = -108; c = +81;
Δ = b2-4ac
Δ = -1082-4·4·81
Δ = 10368
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{10368}=\sqrt{5184*2}=\sqrt{5184}*\sqrt{2}=72\sqrt{2}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-108)-72\sqrt{2}}{2*4}=\frac{108-72\sqrt{2}}{8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-108)+72\sqrt{2}}{2*4}=\frac{108+72\sqrt{2}}{8} $
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