(6x-9)(x-13)=0

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Solution for (6x-9)(x-13)=0 equation:



(6x-9)(x-13)=0
We multiply parentheses ..
(+6x^2-78x-9x+117)=0
We get rid of parentheses
6x^2-78x-9x+117=0
We add all the numbers together, and all the variables
6x^2-87x+117=0
a = 6; b = -87; c = +117;
Δ = b2-4ac
Δ = -872-4·6·117
Δ = 4761
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4761}=69$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-87)-69}{2*6}=\frac{18}{12} =1+1/2 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-87)+69}{2*6}=\frac{156}{12} =13 $

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