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5x(2x-1)=50
We move all terms to the left:
5x(2x-1)-(50)=0
We multiply parentheses
10x^2-5x-50=0
a = 10; b = -5; c = -50;
Δ = b2-4ac
Δ = -52-4·10·(-50)
Δ = 2025
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{2025}=45$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-45}{2*10}=\frac{-40}{20} =-2 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+45}{2*10}=\frac{50}{20} =2+1/2 $
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