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12(x-14)(x+10)=x
We move all terms to the left:
12(x-14)(x+10)-(x)=0
We add all the numbers together, and all the variables
-1x+12(x-14)(x+10)=0
We multiply parentheses ..
12(+x^2+10x-14x-140)-1x=0
We multiply parentheses
12x^2+120x-168x-1x-1680=0
We add all the numbers together, and all the variables
12x^2-49x-1680=0
a = 12; b = -49; c = -1680;
Δ = b2-4ac
Δ = -492-4·12·(-1680)
Δ = 83041
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-49)-\sqrt{83041}}{2*12}=\frac{49-\sqrt{83041}}{24} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-49)+\sqrt{83041}}{2*12}=\frac{49+\sqrt{83041}}{24} $
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