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2x^2-82x+150=0
a = 2; b = -82; c = +150;
Δ = b2-4ac
Δ = -822-4·2·150
Δ = 5524
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{5524}=\sqrt{4*1381}=\sqrt{4}*\sqrt{1381}=2\sqrt{1381}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-82)-2\sqrt{1381}}{2*2}=\frac{82-2\sqrt{1381}}{4} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-82)+2\sqrt{1381}}{2*2}=\frac{82+2\sqrt{1381}}{4} $
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