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27x^2+29x=31
We move all terms to the left:
27x^2+29x-(31)=0
a = 27; b = 29; c = -31;
Δ = b2-4ac
Δ = 292-4·27·(-31)
Δ = 4189
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(29)-\sqrt{4189}}{2*27}=\frac{-29-\sqrt{4189}}{54} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(29)+\sqrt{4189}}{2*27}=\frac{-29+\sqrt{4189}}{54} $
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