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12x^2-32x+5=0
a = 12; b = -32; c = +5;
Δ = b2-4ac
Δ = -322-4·12·5
Δ = 784
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{784}=28$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-28}{2*12}=\frac{4}{24} =1/6 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+28}{2*12}=\frac{60}{24} =2+1/2 $
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