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6x^2+29x-175=0
a = 6; b = 29; c = -175;
Δ = b2-4ac
Δ = 292-4·6·(-175)
Δ = 5041
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{5041}=71$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(29)-71}{2*6}=\frac{-100}{12} =-8+1/3 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(29)+71}{2*6}=\frac{42}{12} =3+1/2 $
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