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5x(2x-1)=8
We move all terms to the left:
5x(2x-1)-(8)=0
We multiply parentheses
10x^2-5x-8=0
a = 10; b = -5; c = -8;
Δ = b2-4ac
Δ = -52-4·10·(-8)
Δ = 345
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{-(-5)-\sqrt{345}}{2*10}=\frac{5-\sqrt{345}}{20} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{345}}{2*10}=\frac{5+\sqrt{345}}{20} $
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