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4x^2+13x=9
We move all terms to the left:
4x^2+13x-(9)=0
a = 4; b = 13; c = -9;
Δ = b2-4ac
Δ = 132-4·4·(-9)
Δ = 313
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{-(13)-\sqrt{313}}{2*4}=\frac{-13-\sqrt{313}}{8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+\sqrt{313}}{2*4}=\frac{-13+\sqrt{313}}{8} $
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