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23x^2-2=5x
We move all terms to the left:
23x^2-2-(5x)=0
a = 23; b = -5; c = -2;
Δ = b2-4ac
Δ = -52-4·23·(-2)
Δ = 209
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{-(-5)-\sqrt{209}}{2*23}=\frac{5-\sqrt{209}}{46} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{209}}{2*23}=\frac{5+\sqrt{209}}{46} $
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