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2x^2-68x-192=0
a = 2; b = -68; c = -192;
Δ = b2-4ac
Δ = -682-4·2·(-192)
Δ = 6160
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{6160}=\sqrt{16*385}=\sqrt{16}*\sqrt{385}=4\sqrt{385}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-68)-4\sqrt{385}}{2*2}=\frac{68-4\sqrt{385}}{4} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-68)+4\sqrt{385}}{2*2}=\frac{68+4\sqrt{385}}{4} $
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