9x(6x+5)=20x

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Solution for 9x(6x+5)=20x equation:



9x(6x+5)=20x
We move all terms to the left:
9x(6x+5)-(20x)=0
We add all the numbers together, and all the variables
-20x+9x(6x+5)=0
We multiply parentheses
54x^2-20x+45x=0
We add all the numbers together, and all the variables
54x^2+25x=0
a = 54; b = 25; c = 0;
Δ = b2-4ac
Δ = 252-4·54·0
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(25)-25}{2*54}=\frac{-50}{108} =-25/54 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+25}{2*54}=\frac{0}{108} =0 $

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