(5x-1)(4x-9)=0

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Solution for (5x-1)(4x-9)=0 equation:



(5x-1)(4x-9)=0
We multiply parentheses ..
(+20x^2-45x-4x+9)=0
We get rid of parentheses
20x^2-45x-4x+9=0
We add all the numbers together, and all the variables
20x^2-49x+9=0
a = 20; b = -49; c = +9;
Δ = b2-4ac
Δ = -492-4·20·9
Δ = 1681
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1681}=41$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-49)-41}{2*20}=\frac{8}{40} =1/5 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-49)+41}{2*20}=\frac{90}{40} =2+1/4 $

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