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8x^2-158x+75=0
a = 8; b = -158; c = +75;
Δ = b2-4ac
Δ = -1582-4·8·75
Δ = 22564
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{22564}=\sqrt{4*5641}=\sqrt{4}*\sqrt{5641}=2\sqrt{5641}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-158)-2\sqrt{5641}}{2*8}=\frac{158-2\sqrt{5641}}{16} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-158)+2\sqrt{5641}}{2*8}=\frac{158+2\sqrt{5641}}{16} $
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