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30x^2-160x+2=0
a = 30; b = -160; c = +2;
Δ = b2-4ac
Δ = -1602-4·30·2
Δ = 25360
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{25360}=\sqrt{16*1585}=\sqrt{16}*\sqrt{1585}=4\sqrt{1585}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-160)-4\sqrt{1585}}{2*30}=\frac{160-4\sqrt{1585}}{60} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-160)+4\sqrt{1585}}{2*30}=\frac{160+4\sqrt{1585}}{60} $
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