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(5a-2)(8a-5)=0
We multiply parentheses ..
(+40a^2-25a-16a+10)=0
We get rid of parentheses
40a^2-25a-16a+10=0
We add all the numbers together, and all the variables
40a^2-41a+10=0
a = 40; b = -41; c = +10;
Δ = b2-4ac
Δ = -412-4·40·10
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{81}=9$$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-41)-9}{2*40}=\frac{32}{80} =2/5 $$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-41)+9}{2*40}=\frac{50}{80} =5/8 $
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