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5x^2-4x-8/10=0
We multiply all the terms by the denominator
5x^2*10-4x*10-8=0
Wy multiply elements
50x^2-40x-8=0
a = 50; b = -40; c = -8;
Δ = b2-4ac
Δ = -402-4·50·(-8)
Δ = 3200
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{3200}=\sqrt{1600*2}=\sqrt{1600}*\sqrt{2}=40\sqrt{2}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-40\sqrt{2}}{2*50}=\frac{40-40\sqrt{2}}{100} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+40\sqrt{2}}{2*50}=\frac{40+40\sqrt{2}}{100} $
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