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(2x+40)(3x-85)=x
We move all terms to the left:
(2x+40)(3x-85)-(x)=0
We add all the numbers together, and all the variables
-1x+(2x+40)(3x-85)=0
We multiply parentheses ..
(+6x^2-170x+120x-3400)-1x=0
We get rid of parentheses
6x^2-170x+120x-1x-3400=0
We add all the numbers together, and all the variables
6x^2-51x-3400=0
a = 6; b = -51; c = -3400;
Δ = b2-4ac
Δ = -512-4·6·(-3400)
Δ = 84201
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{-(-51)-\sqrt{84201}}{2*6}=\frac{51-\sqrt{84201}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-51)+\sqrt{84201}}{2*6}=\frac{51+\sqrt{84201}}{12} $
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