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8x^2-72x+18=0
a = 8; b = -72; c = +18;
Δ = b2-4ac
Δ = -722-4·8·18
Δ = 4608
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{4608}=\sqrt{2304*2}=\sqrt{2304}*\sqrt{2}=48\sqrt{2}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-72)-48\sqrt{2}}{2*8}=\frac{72-48\sqrt{2}}{16} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-72)+48\sqrt{2}}{2*8}=\frac{72+48\sqrt{2}}{16} $
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