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x^2-68x+120=0
a = 1; b = -68; c = +120;
Δ = b2-4ac
Δ = -682-4·1·120
Δ = 4144
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{4144}=\sqrt{16*259}=\sqrt{16}*\sqrt{259}=4\sqrt{259}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-68)-4\sqrt{259}}{2*1}=\frac{68-4\sqrt{259}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-68)+4\sqrt{259}}{2*1}=\frac{68+4\sqrt{259}}{2} $
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