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5x^2+9x=8
We move all terms to the left:
5x^2+9x-(8)=0
a = 5; b = 9; c = -8;
Δ = b2-4ac
Δ = 92-4·5·(-8)
Δ = 241
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{-(9)-\sqrt{241}}{2*5}=\frac{-9-\sqrt{241}}{10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{241}}{2*5}=\frac{-9+\sqrt{241}}{10} $
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