(4x-3)(7x-1)=2x

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Solution for (4x-3)(7x-1)=2x equation:



(4x-3)(7x-1)=2x
We move all terms to the left:
(4x-3)(7x-1)-(2x)=0
We add all the numbers together, and all the variables
-2x+(4x-3)(7x-1)=0
We multiply parentheses ..
(+28x^2-4x-21x+3)-2x=0
We get rid of parentheses
28x^2-4x-21x-2x+3=0
We add all the numbers together, and all the variables
28x^2-27x+3=0
a = 28; b = -27; c = +3;
Δ = b2-4ac
Δ = -272-4·28·3
Δ = 393
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{-(-27)-\sqrt{393}}{2*28}=\frac{27-\sqrt{393}}{56} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+\sqrt{393}}{2*28}=\frac{27+\sqrt{393}}{56} $

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