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(4x-5)(5x-8)=0
We multiply parentheses ..
(+20x^2-32x-25x+40)=0
We get rid of parentheses
20x^2-32x-25x+40=0
We add all the numbers together, and all the variables
20x^2-57x+40=0
a = 20; b = -57; c = +40;
Δ = b2-4ac
Δ = -572-4·20·40
Δ = 49
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{49}=7$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-57)-7}{2*20}=\frac{50}{40} =1+1/4 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-57)+7}{2*20}=\frac{64}{40} =1+3/5 $
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