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23x^2=2
We move all terms to the left:
23x^2-(2)=0
a = 23; b = 0; c = -2;
Δ = b2-4ac
Δ = 02-4·23·(-2)
Δ = 184
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}
The end solution:
\sqrt{\Delta}=\sqrt{184}=\sqrt{4*46}=\sqrt{4}*\sqrt{46}=2\sqrt{46}x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{46}}{2*23}=\frac{0-2\sqrt{46}}{46} =-\frac{2\sqrt{46}}{46} =-\frac{\sqrt{46}}{23}x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{46}}{2*23}=\frac{0+2\sqrt{46}}{46} =\frac{2\sqrt{46}}{46} =\frac{\sqrt{46}}{23}
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