6x(2x-10)+9x=x

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Solution for 6x(2x-10)+9x=x equation:



6x(2x-10)+9x=x
We move all terms to the left:
6x(2x-10)+9x-(x)=0
We add all the numbers together, and all the variables
8x+6x(2x-10)=0
We multiply parentheses
12x^2+8x-60x=0
We add all the numbers together, and all the variables
12x^2-52x=0
a = 12; b = -52; c = 0;
Δ = b2-4ac
Δ = -522-4·12·0
Δ = 2704
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2704}=52$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-52)-52}{2*12}=\frac{0}{24} =0 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-52)+52}{2*12}=\frac{104}{24} =4+1/3 $

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