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(6x-4)(4x+14)=x
We move all terms to the left:
(6x-4)(4x+14)-(x)=0
We add all the numbers together, and all the variables
-1x+(6x-4)(4x+14)=0
We multiply parentheses ..
(+24x^2+84x-16x-56)-1x=0
We get rid of parentheses
24x^2+84x-16x-1x-56=0
We add all the numbers together, and all the variables
24x^2+67x-56=0
a = 24; b = 67; c = -56;
Δ = b2-4ac
Δ = 672-4·24·(-56)
Δ = 9865
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{-(67)-\sqrt{9865}}{2*24}=\frac{-67-\sqrt{9865}}{48} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(67)+\sqrt{9865}}{2*24}=\frac{-67+\sqrt{9865}}{48} $
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