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5x^2-19x=18
We move all terms to the left:
5x^2-19x-(18)=0
a = 5; b = -19; c = -18;
Δ = b2-4ac
Δ = -192-4·5·(-18)
Δ = 721
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{-(-19)-\sqrt{721}}{2*5}=\frac{19-\sqrt{721}}{10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+\sqrt{721}}{2*5}=\frac{19+\sqrt{721}}{10} $
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