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8+5x^2=23x
We move all terms to the left:
8+5x^2-(23x)=0
a = 5; b = -23; c = +8;
Δ = b2-4ac
Δ = -232-4·5·8
Δ = 369
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{369}=\sqrt{9*41}=\sqrt{9}*\sqrt{41}=3\sqrt{41}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-23)-3\sqrt{41}}{2*5}=\frac{23-3\sqrt{41}}{10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+3\sqrt{41}}{2*5}=\frac{23+3\sqrt{41}}{10} $
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