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12x^2-344x+1849=0
a = 12; b = -344; c = +1849;
Δ = b2-4ac
Δ = -3442-4·12·1849
Δ = 29584
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{29584}=172$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-344)-172}{2*12}=\frac{172}{24} =7+1/6 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-344)+172}{2*12}=\frac{516}{24} =21+1/2 $
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