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12x^2-34x+22=0
a = 12; b = -34; c = +22;
Δ = b2-4ac
Δ = -342-4·12·22
Δ = 100
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{100}=10$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-34)-10}{2*12}=\frac{24}{24} =1 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-34)+10}{2*12}=\frac{44}{24} =1+5/6 $
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