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8x^2-23x+10=0
a = 8; b = -23; c = +10;
Δ = b2-4ac
Δ = -232-4·8·10
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{-(-23)-\sqrt{209}}{2*8}=\frac{23-\sqrt{209}}{16} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+\sqrt{209}}{2*8}=\frac{23+\sqrt{209}}{16} $
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