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17x^2-68x+32=0
a = 17; b = -68; c = +32;
Δ = b2-4ac
Δ = -682-4·17·32
Δ = 2448
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{2448}=\sqrt{144*17}=\sqrt{144}*\sqrt{17}=12\sqrt{17}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-68)-12\sqrt{17}}{2*17}=\frac{68-12\sqrt{17}}{34} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-68)+12\sqrt{17}}{2*17}=\frac{68+12\sqrt{17}}{34} $
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