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117x^2-307x+176=0
a = 117; b = -307; c = +176;
Δ = b2-4ac
Δ = -3072-4·117·176
Δ = 11881
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{11881}=109$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-307)-109}{2*117}=\frac{198}{234} =11/13 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-307)+109}{2*117}=\frac{416}{234} =1+7/9 $
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