6x(x-8)-5(x-8)=0

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Solution for 6x(x-8)-5(x-8)=0 equation:



6x(x-8)-5(x-8)=0
We multiply parentheses
6x^2-48x-5x+40=0
We add all the numbers together, and all the variables
6x^2-53x+40=0
a = 6; b = -53; c = +40;
Δ = b2-4ac
Δ = -532-4·6·40
Δ = 1849
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1849}=43$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-53)-43}{2*6}=\frac{10}{12} =5/6 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-53)+43}{2*6}=\frac{96}{12} =8 $

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